glinski_metabolites
tested hypotheses
- observed vivo versus in vitro degradation rates are the same, or observed vivo rates are lower than in vitro rates (due to other degradation processes, uptake kinetics?)
- first order kinetics are michaelis-menton, second order
- are in vitro indicative of in vivo
things to do
- michaelis menton first order comparison for both experiments
- non-linear goodness of fit
install and load supporting libraries
## nodename
## "stp-air"## [1] "R version 3.2.3 (2015-12-10)"##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select##
## 'drc' has been loaded.## Please cite R and 'drc' if used for a publication,## for references type 'citation()' and 'citation('drc')'.## Loading required package: lme4## Loading required package: Matrix## [1] "list of loaded packages: "## [1] "pbkrtest" "lme4" "Matrix" "scatterplot3d"
## [5] "ggplot2" "drc" "MASS" "xtable"
## [9] "zoo" "knitr" "dplyr" "rmarkdown"
## [13] "stats" "graphics" "grDevices" "utils"
## [17] "datasets" "methods" "base"import experimental exposure and microsomal data
Load csv files with experimental data and microsome data sets. The beolw may return false but still be OK if rstudio does not have privileges to data directory (e.g., attached drive).
## [1] "Root directory location: /Users/puruckertom/git/glinski_metabolites/"## [1] "check to see if R can access files OK: TRUE"experimental exposure data structure
Check out structure of imported data sets.
str(micro)## 'data.frame': 352 obs. of 6 variables:
## $ time : int 2 2 2 2 4 4 4 4 12 12 ...
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 1 1 1 1 1 ...
## $ conc : num 3.07 3.69 4.7 1.89 7.62 ...
## $ replicate: int 1 2 3 4 1 2 3 4 1 2 ...Set time and replicate fields as factors for later statistical inference.
microsome experiment data structure
Check out structure of imported data set for the microsome analysis.
str(microsome)## 'data.frame': 1123 obs. of 7 variables:
## $ time : int 0 0 0 15 15 15 30 30 30 60 ...
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 1 level "microsomes": 1 1 1 1 1 1 1 1 1 1 ...
## $ conc : num 1.208 1.596 1.362 0.551 1.347 ...
## $ replicate: int 1 2 3 1 2 3 1 2 3 1 ...
## $ microMexp: num 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 ...Set time and replicate fields as factors for later statistical inference.
## 'data.frame': 1123 obs. of 7 variables:
## $ time : int 0 0 0 15 15 15 30 30 30 60 ...
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 1 level "microsomes": 1 1 1 1 1 1 1 1 1 1 ...
## $ conc : num 1.208 1.596 1.362 0.551 1.347 ...
## $ replicate: Factor w/ 4 levels "1","2","3","4": 1 2 3 1 2 3 1 2 3 1 ...
## $ microMexp: num 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 0.712 ...analyze microsomal data
The microsomal experiment has 3-4 replicates for each pesticide. The experiment progressively increases the concentration of the substrate (microMexp) and measures the enzyme velocity. At each substrate concentration the reaction is quenched after a specific period of time (0, 15, 30, 60, 90 mins). This time series data is used to estimate a slope associated with each substrate concentration. Substrate concentration and linear velocity slopes are then fit using Michaelis-Menten kinetics to estimate reaction rates for each pesticide.
non-linear fitting
We use the dose-response model (drm) package from R for the fitting of the rate constant. We provide it the 2-parameter Michaelis-Menton function (mm2) as an argument. It uses the MM.2 function that is in the drc package and therefore is a drc object that contains a list of class drcMean, containing the mean function, the self starter function, the parameter names and other components such as derivatives and a function for calculating ED values. It is not shifted (??) so uses the fit f(x,(c,d,e)) = c + (d-c)/(1+e/x). Where x is the dose, it is a strictly increasing function so we reverse the sign of the slopes for the parents. e is the dose halfway between c and d, for the 2-parameter model c = 0.
## Michaelis-Menten
## (2 parameters)
## In 'drc': MM.2atrazine
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 0.712"
## ind
## [1,] 1 0 0.7120000
## [2,] 2 0 0.7120000
## [3,] 3 0 0.7120000
## [4,] 4 15 0.5514354
## [5,] 5 15 1.3469113
## [6,] 6 15 1.2124448
## [7,] 7 30 1.1349183
## [8,] 8 30 1.0824669
## [9,] 9 30 1.1138895
## [10,] 10 60 0.9180152
## [11,] 11 60 0.8199161
## [12,] 12 60 0.8304017
## [13,] 13 90 0.6019329
## [14,] 14 90 0.5146155
## [15,] 15 90 0.5430465
## [1] "least squares linear regression for substrate = 0.712"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 0.976685 -0.003153
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37796 -0.22151 0.03239 0.21607 0.41752
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.976685 0.103348 9.450 3.45e-07 ***
## Time[ind] -0.003153 0.002041 -1.545 0.146
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2554 on 13 degrees of freedom
## Multiple R-squared: 0.1551, Adjusted R-squared: 0.09013
## F-statistic: 2.387 on 1 and 13 DF, p-value: 0.1463
##
## (Intercept) Time[ind]
## 0.976685382 -0.003152627
## 2.5 % 97.5 %
## (Intercept) 0.753415733 1.199955031
## Time[ind] -0.007561078 0.001255824
## [1] "weighted linear regression for substrate = 0.712"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.976685382 -0.003152627
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.344
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.37796 -0.22151 0.03239 0.21607 0.41752
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.9767 0.1033 9.4505
## Time[ind] -0.0032 0.0020 -1.5450
##
## Residual standard error: 0.3436 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.976685382 -0.003152627
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## ind
## [1,] 16 0 10.000000
## [2,] 17 0 10.000000
## [3,] 18 0 10.000000
## [4,] 19 15 8.453643
## [5,] 20 15 7.964608
## [6,] 21 15 7.944511
## [7,] 22 30 7.680602
## [8,] 23 30 7.527337
## [9,] 24 30 7.478498
## [10,] 25 60 5.659398
## [11,] 26 60 6.364134
## [12,] 27 60 6.660240
## [13,] 28 60 6.342496
## [14,] 29 90 5.477249
## [15,] 30 90 5.670032
## [1] "least squares linear regression for substrate = 10"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 9.3056 -0.0475
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.7963 -0.3777 -0.1132 0.5429 0.6944
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.305616 0.225240 41.31 3.53e-15 ***
## Time[ind] -0.047498 0.004733 -10.04 1.73e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5487 on 13 degrees of freedom
## Multiple R-squared: 0.8857, Adjusted R-squared: 0.8769
## F-statistic: 100.7 on 1 and 13 DF, p-value: 1.726e-07
##
## (Intercept) Time[ind]
## 9.30561649 -0.04749819
## 2.5 % 97.5 %
## (Intercept) 8.81901420 9.79221878
## Time[ind] -0.05772265 -0.03727374
## [1] "weighted linear regression for substrate = 10"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 9.30561649 -0.04749819
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.662
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.7963 -0.3778 -0.1132 0.5429 0.6944
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 9.3056 0.2252 41.3142
## Time[ind] -0.0475 0.0047 -10.0361
##
## Residual standard error: 0.6619 on 13 degrees of freedom
## (Intercept) Time[ind]
## 9.30561649 -0.04749819
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 3.1684"
## ind
## [1,] 31 0 3.168400
## [2,] 32 0 3.168400
## [3,] 33 0 3.168400
## [4,] 34 15 3.840289
## [5,] 35 15 3.471244
## [6,] 36 15 4.218922
## [7,] 37 30 3.041496
## [8,] 38 30 3.107057
## [9,] 39 30 2.539792
## [10,] 40 60 2.350741
## [11,] 41 60 2.184286
## [12,] 42 60 1.868857
## [13,] 43 90 1.487945
## [14,] 44 90 1.746449
## [15,] 45 90 1.279189
## [1] "least squares linear regression for substrate = 3.1684"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 3.60836 -0.02305
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43996 -0.36681 -0.04111 0.19940 0.95630
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.608360 0.171081 21.091 1.94e-11 ***
## Time[ind] -0.023049 0.003378 -6.823 1.22e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4227 on 13 degrees of freedom
## Multiple R-squared: 0.7817, Adjusted R-squared: 0.7649
## F-statistic: 46.56 on 1 and 13 DF, p-value: 1.218e-05
##
## (Intercept) Time[ind]
## 3.60836007 -0.02304946
## 2.5 % 97.5 %
## (Intercept) 3.23876147 3.97795868
## Time[ind] -0.03034717 -0.01575175
## [1] "weighted linear regression for substrate = 3.1684"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 3.5347402 -0.0221571
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.399
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.36634 -0.33335 -0.02103 0.22144 1.01654
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 3.5347 0.1617 21.8588
## Time[ind] -0.0222 0.0032 -6.9395
##
## Residual standard error: 0.3986 on 13 degrees of freedom
## (Intercept) Time[ind]
## 3.5347402 -0.0221571
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## ind
## [1,] 46 0 50.00000
## [2,] 47 0 50.00000
## [3,] 48 0 50.00000
## [4,] 49 15 30.13526
## [5,] 50 15 28.31361
## [6,] 51 15 26.04382
## [7,] 52 30 30.34766
## [8,] 53 30 27.74702
## [9,] 54 30 25.64127
## [10,] 55 60 28.51624
## [11,] 56 60 26.35221
## [12,] 57 60 24.78296
## [13,] 58 90 26.56519
## [14,] 59 90 24.44743
## [15,] 60 90 24.01566
## [1] "least squares linear regression for substrate = 50"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 39.33 -0.20
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.2839 -5.8864 -0.9746 4.1802 10.6720
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.32803 2.97479 13.220 6.49e-09 ***
## Time[ind] -0.20002 0.05874 -3.405 0.00469 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.35 on 13 degrees of freedom
## Multiple R-squared: 0.4715, Adjusted R-squared: 0.4308
## F-statistic: 11.6 on 1 and 13 DF, p-value: 0.004694
##
## (Intercept) Time[ind]
## 39.3280334 -0.2000208
## 2.5 % 97.5 %
## (Intercept) 32.9013986 45.75466818
## Time[ind] -0.3269145 -0.07312715
## [1] "weighted linear regression for substrate = 50"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 39.3280334 -0.2000208
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 8.27
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -10.2839 -5.8864 -0.9746 4.1802 10.6720
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 39.3280 2.9748 13.2205
## Time[ind] -0.2000 0.0587 -3.4054
##
## Residual standard error: 8.273 on 13 degrees of freedom
## (Intercept) Time[ind]
## 39.3280334 -0.2000208
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## ind
## [1,] 61 0 75.00000
## [2,] 62 0 75.00000
## [3,] 63 0 75.00000
## [4,] 64 15 29.59549
## [5,] 65 15 36.16487
## [6,] 66 15 37.40302
## [7,] 67 30 27.64656
## [8,] 68 30 28.94211
## [9,] 69 30 34.71956
## [10,] 70 60 31.19094
## [11,] 71 60 35.96712
## [12,] 72 60 33.12001
## [13,] 73 90 31.51870
## [14,] 74 90 32.99096
## [15,] 75 90 22.85693
## [1] "least squares linear regression for substrate = 75"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 54.1995 -0.3519
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -19.325 -12.137 0.036 9.729 20.800
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 54.1995 5.8549 9.257 4.37e-07 ***
## Time[ind] -0.3519 0.1156 -3.044 0.0094 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.47 on 13 degrees of freedom
## Multiple R-squared: 0.4162, Adjusted R-squared: 0.3713
## F-statistic: 9.267 on 1 and 13 DF, p-value: 0.009404
##
## (Intercept) Time[ind]
## 54.1995284 -0.3519259
## 2.5 % 97.5 %
## (Intercept) 41.550828 66.8482288
## Time[ind] -0.601674 -0.1021778
## [1] "weighted linear regression for substrate = 75"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 54.1995284 -0.3519259
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 17.1
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -19.32515 -12.13669 0.03604 9.72863 20.80047
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 54.1995 5.8549 9.2572
## Time[ind] -0.3519 0.1156 -3.0442
##
## Residual standard error: 17.08 on 13 degrees of freedom
## (Intercept) Time[ind]
## 54.1995284 -0.3519259
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## ind
## [1,] 76 0 100.00000
## [2,] 77 0 100.00000
## [3,] 78 0 100.00000
## [4,] 79 15 73.12306
## [5,] 80 15 62.97208
## [6,] 81 15 58.17492
## [7,] 82 30 70.93575
## [8,] 83 30 60.89976
## [9,] 84 30 54.39425
## [10,] 85 60 67.30937
## [11,] 86 60 56.75248
## [12,] 87 60 50.73569
## [13,] 88 90 64.11432
## [14,] 89 90 53.06961
## [15,] 90 90 51.00465
## [1] "least squares linear regression for substrate = 100"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 82.6524 -0.3697
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.9313 -10.1962 -0.6243 10.7902 17.3476
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 82.6524 5.3532 15.440 9.66e-10 ***
## Time[ind] -0.3697 0.1057 -3.498 0.00393 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.23 on 13 degrees of freedom
## Multiple R-squared: 0.4849, Adjusted R-squared: 0.4453
## F-statistic: 12.24 on 1 and 13 DF, p-value: 0.003928
##
## (Intercept) Time[ind]
## 82.6523916 -0.3697435
## 2.5 % 97.5 %
## (Intercept) 71.0875829 94.2172003
## Time[ind] -0.5980902 -0.1413968
## [1] "weighted linear regression for substrate = 100"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 82.6523916 -0.3697435
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 15.8
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -18.9313 -10.1962 -0.6243 10.7902 17.3476
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 82.6524 5.3532 15.4399
## Time[ind] -0.3697 0.1057 -3.4981
##
## Residual standard error: 15.8 on 13 degrees of freedom
## (Intercept) Time[ind]
## 82.6523916 -0.3697435
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## ind
## [1,] 91 0 125.00000
## [2,] 92 0 125.00000
## [3,] 93 15 107.97377
## [4,] 94 15 85.24148
## [5,] 95 15 85.54902
## [6,] 96 30 158.65079
## [7,] 97 30 83.63860
## [8,] 98 30 83.07468
## [9,] 99 60 170.65218
## [10,] 100 60 78.21162
## [11,] 101 60 84.54186
## [12,] 102 90 80.88479
## [13,] 103 90 79.00425
## [14,] 104 90 78.20108
## [1] "least squares linear regression for substrate = 125"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 114.3266 -0.2991
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.599 -20.830 -8.809 7.538 74.269
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 114.3266 13.6528 8.374 2.35e-06 ***
## Time[ind] -0.2991 0.2604 -1.148 0.273
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 30.85 on 12 degrees of freedom
## Multiple R-squared: 0.099, Adjusted R-squared: 0.02392
## F-statistic: 1.319 on 1 and 12 DF, p-value: 0.2732
##
## (Intercept) Time[ind]
## 114.3266319 -0.2990577
## 2.5 % 97.5 %
## (Intercept) 84.5797002 144.0735637
## Time[ind] -0.8664937 0.2683783
## [1] "weighted linear regression for substrate = 125"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 110.3197856 -0.3413573
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 21.8
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -19.958 -15.237 -0.995 11.704 80.814
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 110.3198 9.2531 11.9224
## Time[ind] -0.3414 0.1765 -1.9339
##
## Residual standard error: 21.76 on 12 degrees of freedom
## (Intercept) Time[ind]
## 110.3197856 -0.3413573
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## ind
## [1,] 105 0 150.00000
## [2,] 106 0 150.00000
## [3,] 107 0 150.00000
## [4,] 108 0 150.00000
## [5,] 109 15 110.80503
## [6,] 110 15 114.72056
## [7,] 111 15 107.12911
## [8,] 112 15 110.21111
## [9,] 113 30 106.41140
## [10,] 114 30 109.25884
## [11,] 115 30 108.81109
## [12,] 116 30 98.45122
## [13,] 117 60 105.73976
## [14,] 118 60 103.55787
## [15,] 119 60 109.56959
## [16,] 120 60 103.20775
## [17,] 121 90 96.26534
## [18,] 122 90 104.97418
## [19,] 123 90 105.79428
## [20,] 124 90 95.31462
## [1] "least squares linear regression for substrate = 150"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 130.2975 -0.4048
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -19.703 -10.065 -1.362 11.312 19.703
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 130.29755 4.74893 27.437 3.87e-16 ***
## Time[ind] -0.40478 0.09377 -4.317 0.000415 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.55 on 18 degrees of freedom
## Multiple R-squared: 0.5087, Adjusted R-squared: 0.4814
## F-statistic: 18.64 on 1 and 18 DF, p-value: 0.0004153
##
## (Intercept) Time[ind]
## 130.2975485 -0.4047811
## 2.5 % 97.5 %
## (Intercept) 120.3204116 140.2746854
## Time[ind] -0.6017793 -0.2077829
## [1] "weighted linear regression for substrate = 150"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 130.2975485 -0.4047811
##
## Degrees of freedom: 20 total; 18 residual
## Scale estimate: 16.9
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -19.703 -10.065 -1.362 11.312 19.702
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 130.2975 4.7489 27.4372
## Time[ind] -0.4048 0.0938 -4.3169
##
## Residual standard error: 16.94 on 18 degrees of freedom
## (Intercept) Time[ind]
## 130.2975485 -0.4047811
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 200"
## ind
## [1,] 125 0 200.0000
## [2,] 126 0 200.0000
## [3,] 127 0 200.0000
## [4,] 128 15 200.8988
## [5,] 129 15 134.8156
## [6,] 130 15 211.5786
## [7,] 131 30 193.1223
## [8,] 132 30 210.4726
## [9,] 133 30 213.5141
## [10,] 134 60 197.4426
## [11,] 135 60 146.8087
## [12,] 136 60 201.9011
## [13,] 137 90 127.9031
## [14,] 138 90 203.6292
## [15,] 139 90 128.0068
## [1] "least squares linear regression for substrate = 200"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 202.5624 -0.4587
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -60.866 -15.397 4.321 22.037 42.350
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 202.5624 11.8464 17.099 2.72e-10 ***
## Time[ind] -0.4587 0.2339 -1.961 0.0717 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 29.27 on 13 degrees of freedom
## Multiple R-squared: 0.2283, Adjusted R-squared: 0.1689
## F-statistic: 3.846 on 1 and 13 DF, p-value: 0.07165
##
## (Intercept) Time[ind]
## 202.5623712 -0.4587044
## 2.5 % 97.5 %
## (Intercept) 176.9698580 228.15488441
## Time[ind] -0.9640276 0.04661879
## [1] "weighted linear regression for substrate = 200"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 205.0357007 -0.4886842
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 32.2
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -62.890 -16.971 2.747 20.913 42.575
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 205.0357 11.5896 17.6913
## Time[ind] -0.4887 0.2288 -2.1355
##
## Residual standard error: 32.21 on 13 degrees of freedom
## (Intercept) Time[ind]
## 205.0357007 -0.4886842
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## ind
## [1,] 140 0 250.0000
## [2,] 141 0 250.0000
## [3,] 142 0 250.0000
## [4,] 143 15 111.0650
## [5,] 144 15 110.3942
## [6,] 145 15 107.7700
## [7,] 146 30 110.0390
## [8,] 147 31 133.1637
## [9,] 148 30 106.6453
## [10,] 149 60 125.4094
## [11,] 150 60 132.3152
## [12,] 151 60 129.5529
## [13,] 152 90 107.9475
## [14,] 153 90 109.2892
## [15,] 154 90 110.9269
## [1] "least squares linear regression for substrate = 250"
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Coefficients:
## (Intercept) Time[ind]
## 181.5297 -0.9871
##
##
## Call:
## lm(formula = Observed[ind] ~ Time[ind])
##
## Residuals:
## Min 1Q Median 3Q Max
## -58.954 -43.575 7.248 17.415 68.470
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 181.5297 19.1185 9.495 3.27e-07 ***
## Time[ind] -0.9871 0.3772 -2.617 0.0213 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 47.18 on 13 degrees of freedom
## Multiple R-squared: 0.345, Adjusted R-squared: 0.2946
## F-statistic: 6.848 on 1 and 13 DF, p-value: 0.02131
##
## (Intercept) Time[ind]
## 181.5296510 -0.9870757
## 2.5 % 97.5 %
## (Intercept) 140.226690 222.832612
## Time[ind] -1.801955 -0.172196
## [1] "weighted linear regression for substrate = 250"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 181.5296510 -0.9870757
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 62.1
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -58.954 -43.575 7.248 17.415 68.470
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 181.5297 19.1185 9.4950
## Time[ind] -0.9871 0.3772 -2.6169
##
## Residual standard error: 62.09 on 13 degrees of freedom
## (Intercept) Time[ind]
## 181.5296510 -0.9870757
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 10 obs. of 2 variables:
## $ sub: num 0.712 10 3.168 50 75 ...
## $ vel: num 15.8 237.5 110.8 1000.1 1759.6 ...## sub vel
## 1 0.7120 15.76313
## 2 10.0000 237.49097
## 3 3.1684 110.78549
## 4 50.0000 1000.10406
## 5 75.0000 1759.62962
## 6 100.0000 1848.71748
## 7 125.0000 1706.78667
## 8 150.0000 2023.90534
## 9 200.0000 2443.42089
## 10 250.0000 4935.37833
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 1.1875e+05 2.9122e+05 4.0778e-01 0.6941
## e:(Intercept) 7.0431e+03 1.7722e+04 3.9742e-01 0.7015
##
## Residual standard error:
##
## 513.6883 (8 degrees of freedom)
We are interested in the reaction rate, v, which is a function of available substrate (pesticide) and the presence of an enzyme. We get Vmax from the asymptote and K = 0.5*Vmax. Biochemical reactions with a single substrate are typically assumed to follow Michaelis-Menten kinetics even if they deviate from the basic model assumptions.
We are fitting the 2-parameter model.
Used to estimate slopes.
dea
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.105334715" "Concs = 0.177716074" "Concs = 0.215668236"
## [7] "Concs = 0.273065521" "Concs = 0.362248011" "Concs = 0.403265809"
## [10] "Concs = 0.502168642" "Concs = 0.64289193" "Concs = 0.720570734"
## [13] "Concs = 0.725802164" "Concs = 0.865500124" "Concs = 0.956691847"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 8 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.023932957 0.009657919
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0695
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.16734 -0.03413 -0.02393 0.04772 0.11716
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0239 0.0333 0.7179
## Time[ind] 0.0097 0.0007 14.6730
##
## Residual standard error: 0.06948 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.023932957 0.009657919
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.062527948" "Concs = 0.066722432" "Concs = 0.073739184"
## [7] "Concs = 0.13417786" "Concs = 0.142144514" "Concs = 0.153899766"
## [10] "Concs = 0.359398841" "Concs = 0.284549411" "Concs = 0.293488967"
## [13] "Concs = 0.291970799" "Concs = 0.378114427" "Concs = 0.405964967"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.002435634 0.004635853
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0109
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.041548 -0.006292 -0.002436 0.007673 0.078812
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0024 0.0048 0.5086
## Time[ind] 0.0046 0.0001 46.0686
##
## Residual standard error: 0.01087 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.002435634 0.004635853
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 31" "Indices = 32" "Indices = 33" "Indices = 34"
## [5] "Indices = 35" "Indices = 36" "Indices = 37" "Indices = 38"
## [9] "Indices = 39" "Indices = 40" "Indices = 41" "Indices = 42"
## [13] "Indices = 43" "Indices = 44" "Indices = 45"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.692469949" "Concs = 0.598237597" "Concs = 0.603481745"
## [7] "Concs = 1.23886552" "Concs = 1.156190328" "Concs = 1.011651128"
## [10] "Concs = 2.056702931" "Concs = 1.850305243" "Concs = 1.516060546"
## [13] "Concs = 2.637550555" "Concs = 2.271829323" "Concs = 2.15464298"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.1946066 0.0254169
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.289
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.32748 -0.19461 0.02762 0.14305 0.33708
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.1946 0.0868 2.2415
## Time[ind] 0.0254 0.0017 14.8270
##
## Residual standard error: 0.2885 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.1946066 0.0254169
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 46" "Indices = 47" "Indices = 48" "Indices = 49"
## [5] "Indices = 50" "Indices = 51" "Indices = 52" "Indices = 53"
## [9] "Indices = 54" "Indices = 55" "Indices = 56" "Indices = 57"
## [13] "Indices = 58" "Indices = 59" "Indices = 60"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.126910879" "Concs = 0.194298986" "Concs = 0.205689666"
## [7] "Concs = 0.343048244" "Concs = 0.344665429" "Concs = 0.433300567"
## [10] "Concs = 0.79823473" "Concs = 0.910129645" "Concs = 0.789753599"
## [13] "Concs = 1.097803094" "Concs = 1.250836941" "Concs = 0.891346428"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 11 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## -0.004886745 0.012957863
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0581
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.269974 -0.039992 0.004887 0.021409 0.137545
##
## Coefficients:
## Value Std. Error t value
## (Intercept) -0.0049 0.0265 -0.1845
## Time[ind] 0.0130 0.0005 24.7777
##
## Residual standard error: 0.05809 on 13 degrees of freedom
## (Intercept) Time[ind]
## -0.004886745 0.012957863
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 61" "Indices = 62" "Indices = 63" "Indices = 64"
## [5] "Indices = 65" "Indices = 66" "Indices = 67" "Indices = 68"
## [9] "Indices = 69" "Indices = 70" "Indices = 71" "Indices = 72"
## [13] "Indices = 73"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.660583406" "Concs = 0.521827731" "Concs = 0.519014334"
## [7] "Concs = 0.937060708" "Concs = 0.947234926" "Concs = 1.586433592"
## [10] "Concs = 1.701961252" "Concs = 2.098184546" "Concs = 2.114078113"
## [13] "Concs = 1.9947066"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.15066966 0.02246945
##
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 0.182
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.1782 -0.1507 0.0313 0.1123 0.2031
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.1507 0.0584 2.5779
## Time[ind] 0.0225 0.0011 19.6538
##
## Residual standard error: 0.1816 on 11 degrees of freedom
## (Intercept) Time[ind]
## 0.15066966 0.02246945
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 0.712"
## [1] "Indices = 74" "Indices = 75" "Indices = 76" "Indices = 77"
## [5] "Indices = 78" "Indices = 79" "Indices = 80" "Indices = 81"
## [9] "Indices = 82" "Indices = 83" "Indices = 84" "Indices = 85"
## [13] "Indices = 86" "Indices = 87"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 0 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0 0
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## 0 0 0 0 0
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0 NaN NaN
## Time[ind] 0 NaN NaN
##
## Residual standard error: 0 on 12 degrees of freedom
## (Intercept) Time[ind]
## 0 0
## 2.5 % 97.5 %
## (Intercept) NaN NaN
## Time[ind] NaN NaN
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 3.1684"
## [1] "Indices = 88" "Indices = 89" "Indices = 90" "Indices = 91"
## [5] "Indices = 92" "Indices = 93" "Indices = 94" "Indices = 95"
## [9] "Indices = 96" "Indices = 97" "Indices = 98" "Indices = 99"
## [13] "Indices = 100" "Indices = 101" "Indices = 102"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0" "Concs = 0"
## [7] "Concs = 0" "Concs = 0" "Concs = 0"
## [10] "Concs = 0.004276181" "Concs = 0" "Concs = 0"
## [13] "Concs = 0.068958259" "Concs = 0.095246481" "Concs = 0.042564751"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 16 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## -0.0090857770 0.0005150538
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0135
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.021817 -0.006366 0.001360 0.009086 0.057977
##
## Coefficients:
## Value Std. Error t value
## (Intercept) -0.0091 0.0072 -1.2543
## Time[ind] 0.0005 0.0001 3.6012
##
## Residual standard error: 0.01347 on 13 degrees of freedom
## (Intercept) Time[ind]
## -0.0090857770 0.0005150538
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 200"
## [1] "Indices = 103" "Indices = 104" "Indices = 105" "Indices = 106"
## [5] "Indices = 107" "Indices = 108" "Indices = 109" "Indices = 110"
## [9] "Indices = 111" "Indices = 112" "Indices = 113" "Indices = 114"
## [13] "Indices = 115" "Indices = 116" "Indices = 117"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0" "Concs = 0"
## [7] "Concs = 0" "Concs = 0" "Concs = 0"
## [10] "Concs = 0" "Concs = 0.08814803" "Concs = 0"
## [13] "Concs = 0.636612173" "Concs = 0.308057976" "Concs = 0.343301822"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 7 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## -0.060061083 0.003574623
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.089
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.154416 -0.047178 0.006442 0.060061 0.374957
##
## Coefficients:
## Value Std. Error t value
## (Intercept) -0.0601 0.0395 -1.5207
## Time[ind] 0.0036 0.0008 4.5837
##
## Residual standard error: 0.08905 on 13 degrees of freedom
## (Intercept) Time[ind]
## -0.060061083 0.003574623
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 118" "Indices = 119" "Indices = 120" "Indices = 121"
## [5] "Indices = 122" "Indices = 123" "Indices = 124" "Indices = 125"
## [9] "Indices = 126" "Indices = 127" "Indices = 128" "Indices = 129"
## [13] "Indices = 130"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.303186347" "Concs = 0.314346484" "Concs = 0.32890249"
## [7] "Concs = 0.470955087" "Concs = 0.418661875" "Concs = 0.69686814"
## [10] "Concs = 0.65732937" "Concs = 1.058297138" "Concs = 1.054151944"
## [13] "Concs = 0.826804017"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.08439208 0.01021475
##
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 0.114
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.17692 -0.08439 0.02783 0.06557 0.09129
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0844 0.0383 2.2006
## Time[ind] 0.0102 0.0008 13.6170
##
## Residual standard error: 0.1138 on 11 degrees of freedom
## (Intercept) Time[ind]
## 0.08439208 0.01021475
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 131" "Indices = 132" "Indices = 133" "Indices = 134"
## [5] "Indices = 135" "Indices = 136" "Indices = 137" "Indices = 138"
## [9] "Indices = 139" "Indices = 140" "Indices = 141" "Indices = 142"
## [13] "Indices = 143" "Indices = 144" "Indices = 145" "Indices = 146"
## [17] "Indices = 147" "Indices = 148"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 0" "Times = 15"
## [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0.651134538" "Concs = 0.410418033"
## [7] "Concs = 0.72633168" "Concs = 0.655344167" "Concs = 1.213331632"
## [10] "Concs = 0.938854783" "Concs = 1.336588359" "Concs = 1.220393789"
## [13] "Concs = 2.258618197" "Concs = 2.185187246" "Concs = 2.037689206"
## [16] "Concs = 2.794152863" "Concs = 2.97663412" "Concs = 2.702787847"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.11936774 0.03168274
##
## Degrees of freedom: 18 total; 16 residual
## Scale estimate: 0.195
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.26803 -0.11937 0.01159 0.14054 0.26674
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.1194 0.0661 1.8051
## Time[ind] 0.0317 0.0014 22.4729
##
## Residual standard error: 0.1947 on 16 degrees of freedom
## (Intercept) Time[ind]
## 0.11936774 0.03168274
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 10 obs. of 2 variables:
## $ sub: num 50 10 100 75 125 ...
## $ vel: num 48.3 23.2 127.1 64.8 112.3 ...## sub vel
## 1 50.0000 48.289594
## 2 10.0000 23.179265
## 3 100.0000 127.084516
## 4 75.0000 64.789315
## 5 125.0000 112.347269
## 6 0.7120 0.000000
## 7 3.1684 2.575269
## 8 200.0000 17.873113
## 9 250.0000 51.073730
## 10 150.0000 158.413706
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 97.64281 29.77021 3.27988 0.0112
## e:(Intercept) 21.13369 29.70447 0.71146 0.4970
##
## Residual standard error:
##
## 44.01437 (8 degrees of freedom)
We are interested in the reaction rate, v, which is a function of available substrate (pesticide) and the presence of an enzyme. We get Vmax from the asymptote and K = 0.5*Vmax. Biochemical reactions with a single substrate are typically assumed to follow Michaelis-Menten kinetics even if they deviate from the basic model assumptions.
We are fitting the 2-parameter model.
Used to estimate slopes.
dia
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.17588934" "Concs = 0.162027282" "Concs = 0.163356559"
## [7] "Concs = 0.343213005" "Concs = 0.307927387" "Concs = 0.309459105"
## [10] "Concs = 0.560097677" "Concs = 0.54821645" "Concs = 0.533109282"
## [13] "Concs = 0.73827321" "Concs = 0.728694143" "Concs = 0.726811372"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 3 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.039703425 0.008028213
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0429
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.03970 -0.03449 0.00323 0.02710 0.06266
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0397 0.0150 2.6499
## Time[ind] 0.0080 0.0003 27.1369
##
## Residual standard error: 0.04286 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.039703425 0.008028213
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 60" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.037225886" "Concs = 0.038369499" "Concs = 0.046312162"
## [7] "Concs = 0.08490015" "Concs = 0.083838648" "Concs = 0.093345378"
## [10] "Concs = 0.209721193" "Concs = 0.168743119" "Concs = 0.161851994"
## [13] "Concs = 0.162150446" "Concs = 0.222852555" "Concs = 0.229604672"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 14 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.003164745 0.002624622
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0056
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.016528 -0.003665 0.001210 0.003387 0.049079
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0032 0.0036 0.8757
## Time[ind] 0.0026 0.0001 34.5621
##
## Residual standard error: 0.005601 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.003164745 0.002624622
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 31" "Indices = 32" "Indices = 33" "Indices = 34"
## [5] "Indices = 35" "Indices = 36" "Indices = 37" "Indices = 38"
## [9] "Indices = 39" "Indices = 40" "Indices = 41" "Indices = 42"
## [13] "Indices = 43" "Indices = 44" "Indices = 45"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.519984026" "Concs = 0.456185794" "Concs = 0.465640368"
## [7] "Concs = 0.969762496" "Concs = 0.925948373" "Concs = 0.828633383"
## [10] "Concs = 1.646101156" "Concs = 1.493978674" "Concs = 1.273473826"
## [13] "Concs = 2.097846916" "Concs = 1.845660879" "Concs = 1.775884862"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.14326104 0.02076955
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.212
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.23664 -0.14326 0.01084 0.09494 0.25667
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.1433 0.0633 2.2631
## Time[ind] 0.0208 0.0012 16.6170
##
## Residual standard error: 0.2124 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.14326104 0.02076955
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 46" "Indices = 47" "Indices = 48" "Indices = 49"
## [5] "Indices = 50" "Indices = 51" "Indices = 52" "Indices = 53"
## [9] "Indices = 54" "Indices = 55" "Indices = 56" "Indices = 57"
## [13] "Indices = 58" "Indices = 59" "Indices = 60"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.105167732" "Concs = 0.164272494" "Concs = 0.177858813"
## [7] "Concs = 0.289730134" "Concs = 0.302066953" "Concs = 0.387892352"
## [10] "Concs = 0.703975509" "Concs = 0.8027739" "Concs = 0.718751156"
## [13] "Concs = 0.974859321" "Concs = 1.104369407" "Concs = 0.769135715"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## -0.008202928 0.011576043
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0549
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.264505 -0.043180 0.008203 0.025004 0.116414
##
## Coefficients:
## Value Std. Error t value
## (Intercept) -0.0082 0.0233 -0.3526
## Time[ind] 0.0116 0.0005 25.2030
##
## Residual standard error: 0.05487 on 13 degrees of freedom
## (Intercept) Time[ind]
## -0.008202928 0.011576043
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 61" "Indices = 62" "Indices = 63" "Indices = 64"
## [5] "Indices = 65" "Indices = 66" "Indices = 67" "Indices = 68"
## [9] "Indices = 69" "Indices = 70" "Indices = 71" "Indices = 72"
## [13] "Indices = 73"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.558156141" "Concs = 0.453398653" "Concs = 0.457441572"
## [7] "Concs = 0.819739976" "Concs = 0.818340148" "Concs = 1.39707951"
## [10] "Concs = 1.483198815" "Concs = 1.818559552" "Concs = 1.850457042"
## [13] "Concs = 1.741234977"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.1293156 0.0196293
##
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 0.151
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.15472 -0.12932 0.02964 0.10015 0.17613
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.1293 0.0504 2.5660
## Time[ind] 0.0196 0.0010 19.9121
##
## Residual standard error: 0.1505 on 11 degrees of freedom
## (Intercept) Time[ind]
## 0.1293156 0.0196293
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 0.712"
## [1] "Indices = 74" "Indices = 75" "Indices = 76" "Indices = 77"
## [5] "Indices = 78" "Indices = 79" "Indices = 80" "Indices = 81"
## [9] "Indices = 82" "Indices = 83" "Indices = 84" "Indices = 85"
## [13] "Indices = 86" "Indices = 87" "Indices = 88"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 0 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0 0
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## 0 0 0 0 0
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0 NaN NaN
## Time[ind] 0 NaN NaN
##
## Residual standard error: 0 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0 0
## 2.5 % 97.5 %
## (Intercept) NaN NaN
## Time[ind] NaN NaN
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 3.1684"
## [1] "Indices = 89" "Indices = 90" "Indices = 91" "Indices = 92"
## [5] "Indices = 93" "Indices = 94" "Indices = 95" "Indices = 96"
## [9] "Indices = 97" "Indices = 98" "Indices = 99" "Indices = 100"
## [13] "Indices = 101" "Indices = 102" "Indices = 103"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [6] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## [11] "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0" "Concs = 0"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 0 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0 0
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## 0 0 0 0 0
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0 NaN NaN
## Time[ind] 0 NaN NaN
##
## Residual standard error: 0 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0 0
## 2.5 % 97.5 %
## (Intercept) NaN NaN
## Time[ind] NaN NaN
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 104" "Indices = 105" "Indices = 106" "Indices = 107"
## [5] "Indices = 108" "Indices = 109" "Indices = 110" "Indices = 111"
## [9] "Indices = 112" "Indices = 113" "Indices = 114" "Indices = 115"
## [13] "Indices = 116"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.488073154" "Concs = 0.494203709" "Concs = 0.58569046"
## [7] "Concs = 0.731173258" "Concs = 0.714667917" "Concs = 1.145221545"
## [10] "Concs = 1.154181588" "Concs = 1.638731263" "Concs = 1.563749853"
## [13] "Concs = 1.475092589"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 3 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.1502412 0.0162300
##
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 0.14
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.15024 -0.13585 0.02779 0.09403 0.19200
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.1502 0.0550 2.7302
## Time[ind] 0.0162 0.0011 15.0778
##
## Residual standard error: 0.1399 on 11 degrees of freedom
## (Intercept) Time[ind]
## 0.1502412 0.0162300
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 117" "Indices = 118" "Indices = 119" "Indices = 120"
## [5] "Indices = 121" "Indices = 122" "Indices = 123" "Indices = 124"
## [9] "Indices = 125" "Indices = 126" "Indices = 127" "Indices = 128"
## [13] "Indices = 129" "Indices = 130" "Indices = 131" "Indices = 132"
## [17] "Indices = 133" "Indices = 134"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 0" "Times = 15"
## [6] "Times = 15" "Times = 15" "Times = 15" "Times = 30" "Times = 30"
## [11] "Times = 30" "Times = 30" "Times = 60" "Times = 60" "Times = 60"
## [16] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0.462309631" "Concs = 0.255700106"
## [7] "Concs = 0.526463046" "Concs = 0.47230486" "Concs = 0.931548447"
## [10] "Concs = 0.722337549" "Concs = 1.066740758" "Concs = 0.948249061"
## [13] "Concs = 1.827879364" "Concs = 1.789768545" "Concs = 1.614786398"
## [16] "Concs = 2.243971727" "Concs = 2.385364241" "Concs = 2.16439478"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.06159826 0.02581150
##
## Degrees of freedom: 18 total; 16 residual
## Scale estimate: 0.128
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.220238 -0.061598 0.002615 0.091127 0.230798
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0616 0.0609 1.0121
## Time[ind] 0.0258 0.0013 19.8930
##
## Residual standard error: 0.1285 on 16 degrees of freedom
## (Intercept) Time[ind]
## 0.06159826 0.02581150
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 200"
## [1] "Indices = 135" "Indices = 136" "Indices = 137" "Indices = 138"
## [5] "Indices = 139" "Indices = 140" "Indices = 141" "Indices = 142"
## [9] "Indices = 143" "Indices = 144" "Indices = 145" "Indices = 146"
## [13] "Indices = 147" "Indices = 148" "Indices = 149"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0" "Concs = 0"
## [7] "Concs = 0" "Concs = 0" "Concs = 0"
## [10] "Concs = 0.147179292" "Concs = 0.49374336" "Concs = 0.185151589"
## [13] "Concs = 0.905020781" "Concs = 0.751527127" "Concs = 0.778803003"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## -0.135091948 0.009038982
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.2
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.2600677 -0.1360775 -0.0004928 0.1177393 0.2266044
##
## Coefficients:
## Value Std. Error t value
## (Intercept) -0.1351 0.0616 -2.1918
## Time[ind] 0.0090 0.0012 7.4273
##
## Residual standard error: 0.2003 on 13 degrees of freedom
## (Intercept) Time[ind]
## -0.135091948 0.009038982
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 10 obs. of 2 variables:
## $ sub: num 50 10 100 75 125 ...
## $ vel: num 40.1 13.1 103.8 57.9 98.1 ...## sub vel
## 1 50.0000 40.14107
## 2 10.0000 13.12311
## 3 100.0000 103.84774
## 4 75.0000 57.88021
## 5 125.0000 98.14650
## 6 0.7120 0.00000
## 7 3.1684 0.00000
## 8 250.0000 81.14999
## 9 150.0000 129.05748
## 10 200.0000 45.19491
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 110.1071 29.6962 3.7078 0.0060
## e:(Intercept) 44.4716 40.7922 1.0902 0.3074
##
## Residual standard error:
##
## 26.75434 (8 degrees of freedom)
triadimefon
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 0.68082"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0.68082" "Concs = 0.68082" "Concs = 0.68082"
## [4] "Concs = 0.399443695" "Concs = 0.42224169" "Concs = 0.36799564"
## [7] "Concs = 0.335043095" "Concs = 0.307545884" "Concs = 0.33049829"
## [10] "Concs = 0.298781298" "Concs = 0.300851183" "Concs = 0.297372843"
## [13] "Concs = 0.30988245" "Concs = 0.29724505" "Concs = 0.293730776"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.530169234 -0.003332387
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.12
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.12265 -0.08795 -0.03144 0.07331 0.15065
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.5302 0.0424 12.5176
## Time[ind] -0.0033 0.0008 -3.9848
##
## Residual standard error: 0.1197 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.530169234 -0.003332387
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 10" "Concs = 10" "Concs = 10"
## [4] "Concs = 3.796829723" "Concs = 3.995422538" "Concs = 4.084402023"
## [7] "Concs = 3.689670522" "Concs = 3.770627455" "Concs = 3.708045842"
## [10] "Concs = 2.923805377" "Concs = 2.81999575" "Concs = 1.627429272"
## [13] "Concs = 1.556106647" "Concs = 1.615639352"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 7.24519589 -0.07208527
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 2.05
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -2.36709 -1.38837 -0.04818 0.86696 2.75480
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 7.2452 0.7850 9.2290
## Time[ind] -0.0721 0.0157 -4.5830
##
## Residual standard error: 2.052 on 12 degrees of freedom## (Intercept) Time[ind]
## 7.24519589 -0.07208527
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 30" "Indices = 31" "Indices = 32" "Indices = 33"
## [5] "Indices = 34" "Indices = 35" "Indices = 36" "Indices = 37"
## [9] "Indices = 38" "Indices = 39" "Indices = 40" "Indices = 41"
## [13] "Indices = 42" "Indices = 43" "Indices = 44"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 2.89" "Concs = 2.89" "Concs = 2.89"
## [4] "Concs = 1.438977536" "Concs = 1.147878572" "Concs = 1.273836719"
## [7] "Concs = 1.170628317" "Concs = 1.153347335" "Concs = 0.90609785"
## [10] "Concs = 0.796555881" "Concs = 0.724314066" "Concs = 0.705525399"
## [13] "Concs = 0.684015583" "Concs = 0.645877009" "Concs = 0.633912406"## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Ran 20 iterations without convergence
##
## Coefficients:
## (Intercept) Time[ind]
## 1.74179311 -0.01438885
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.296
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.40403 -0.16486 -0.08698 0.21815 1.14821
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 1.7418 0.1676 10.3908
## Time[ind] -0.0144 0.0033 -4.3473
##
## Residual standard error: 0.2961 on 13 degrees of freedom
## (Intercept) Time[ind]
## 1.74179311 -0.01438885
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 45" "Indices = 46" "Indices = 47" "Indices = 48"
## [5] "Indices = 49" "Indices = 50" "Indices = 51" "Indices = 52"
## [9] "Indices = 53" "Indices = 54" "Indices = 55" "Indices = 56"
## [13] "Indices = 57"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 50" "Concs = 50" "Concs = 50"
## [4] "Concs = 25.6223204" "Concs = 24.15898057" "Concs = 24.97516518"
## [7] "Concs = 26.62994332" "Concs = 26.25228145" "Concs = 25.95782864"
## [10] "Concs = 28.59868326" "Concs = 22.32352998" "Concs = 22.61126729"
## [13] "Concs = 22.93204565"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 38.6877394 -0.2078355
##
## Degrees of freedom: 13 total; 11 residual
## Scale estimate: 9.19
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -11.411 -6.200 2.341 2.950 11.312
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 38.6877 3.5986 10.7508
## Time[ind] -0.2078 0.0704 -2.9525
##
## Residual standard error: 9.193 on 11 degrees of freedom## (Intercept) Time[ind]
## 38.6877394 -0.2078355
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 58" "Indices = 59" "Indices = 60" "Indices = 61"
## [5] "Indices = 62" "Indices = 63" "Indices = 64" "Indices = 65"
## [9] "Indices = 66" "Indices = 67" "Indices = 68" "Indices = 69"
## [13] "Indices = 70" "Indices = 71" "Indices = 72"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 75" "Concs = 75" "Concs = 75"
## [4] "Concs = 39.60290919" "Concs = 36.37647057" "Concs = 38.41537648"
## [7] "Concs = 41.36228948" "Concs = 39.60347726" "Concs = 37.05197615"
## [10] "Concs = 38.79077057" "Concs = 39.14694989" "Concs = 38.88285882"
## [13] "Concs = 38.84162326" "Concs = 38.38496898" "Concs = 38.08875118"## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Ran 20 iterations without convergence
##
## Coefficients:
## (Intercept) Time[ind]
## 43.56867863 -0.07261069
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 3.13
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -6.10305 -2.33174 -0.06509 1.57958 31.43132
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 43.5687 2.0022 21.7602
## Time[ind] -0.0726 0.0395 -1.8367
##
## Residual standard error: 3.132 on 13 degrees of freedom
## (Intercept) Time[ind]
## 43.56867863 -0.07261069
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 73" "Indices = 74" "Indices = 75" "Indices = 76"
## [5] "Indices = 77" "Indices = 78" "Indices = 79" "Indices = 80"
## [9] "Indices = 81" "Indices = 82" "Indices = 83" "Indices = 84"
## [13] "Indices = 85" "Indices = 86" "Indices = 87"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 100" "Concs = 100" "Concs = 100"
## [4] "Concs = 49.24893567" "Concs = 52.23999837" "Concs = 54.94800062"
## [7] "Concs = 51.63283427" "Concs = 55.62979138" "Concs = 53.25296347"
## [10] "Concs = 57.2285182" "Concs = 52.25557462" "Concs = 57.56142454"
## [13] "Concs = 55.15134637" "Concs = 52.80788424" "Concs = 54.77096052"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 75.7962700 -0.3251552
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 19
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -21.6700 -13.5987 0.9416 8.4289 24.2037
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 75.7963 6.6510 11.3963
## Time[ind] -0.3252 0.1313 -2.4760
##
## Residual standard error: 18.96 on 13 degrees of freedom
## (Intercept) Time[ind]
## 75.7962700 -0.3251552
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 88" "Indices = 89" "Indices = 90" "Indices = 91"
## [5] "Indices = 92" "Indices = 93" "Indices = 94" "Indices = 95"
## [9] "Indices = 96" "Indices = 97" "Indices = 98" "Indices = 99"
## [13] "Indices = 100" "Indices = 101"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 125" "Concs = 125" "Concs = 125"
## [4] "Concs = 54.97761564" "Concs = 64.19295623" "Concs = 61.97688614"
## [7] "Concs = 68.89112849" "Concs = 56.33566744" "Concs = 71.31751913"
## [10] "Concs = 66.04862513" "Concs = 69.71262134" "Concs = 57.48171016"
## [13] "Concs = 60.79276739" "Concs = 57.42314849"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 94.1185302 -0.4828739
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 24.8
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -31.898 -19.697 2.735 9.305 30.881
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 94.1185 9.0233 10.4306
## Time[ind] -0.4829 0.1808 -2.6709
##
## Residual standard error: 24.78 on 12 degrees of freedom## (Intercept) Time[ind]
## 94.1185302 -0.4828739
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 102" "Indices = 103" "Indices = 104" "Indices = 105"
## [5] "Indices = 106" "Indices = 107" "Indices = 108" "Indices = 109"
## [9] "Indices = 110" "Indices = 111" "Indices = 112" "Indices = 113"
## [13] "Indices = 114" "Indices = 115"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 150" "Concs = 150" "Concs = 78.63355587"
## [4] "Concs = 62.93987056" "Concs = 106.7018113" "Concs = 73.37624336"
## [7] "Concs = 66.9635187" "Concs = 95.5133834" "Concs = 69.7678651"
## [10] "Concs = 58.53815945" "Concs = 61.06336245" "Concs = 82.43537943"
## [13] "Concs = 75.76324133" "Concs = 73.77914496"## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Ran 20 iterations without convergence
##
## Coefficients:
## (Intercept) Time[ind]
## 101.3079410 -0.4215165
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 23.5
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -32.0453 -16.0853 0.3009 12.2230 48.6921
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 101.3079 12.3785 8.1842
## Time[ind] -0.4215 0.2361 -1.7851
##
## Residual standard error: 23.47 on 12 degrees of freedom
## (Intercept) Time[ind]
## 101.3079410 -0.4215165
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 200"
## [1] "Indices = 116" "Indices = 117" "Indices = 118" "Indices = 119"
## [5] "Indices = 120" "Indices = 121" "Indices = 122" "Indices = 123"
## [9] "Indices = 124" "Indices = 125" "Indices = 126" "Indices = 127"
## [13] "Indices = 128" "Indices = 129" "Indices = 130"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 200" "Concs = 200" "Concs = 200"
## [4] "Concs = 338.7826757" "Concs = 357.9520843" "Concs = 202.0964578"
## [7] "Concs = 422.3552358" "Concs = 340.5253492" "Concs = 345.8291382"
## [10] "Concs = 359.4674526" "Concs = 377.2730298" "Concs = 186.1093226"
## [13] "Concs = 471.6047045" "Concs = 376.1365036" "Concs = 190.6933116"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 9 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 255.779660 1.454499
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 82.7
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -195.99 -55.78 16.42 53.80 122.94
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 255.7797 39.7870 6.4287
## Time[ind] 1.4545 0.7856 1.8515
##
## Residual standard error: 82.7 on 13 degrees of freedom
## (Intercept) Time[ind]
## 255.779660 1.454499
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 131" "Indices = 132" "Indices = 133" "Indices = 134"
## [5] "Indices = 135" "Indices = 136" "Indices = 137" "Indices = 138"
## [9] "Indices = 139" "Indices = 140" "Indices = 141" "Indices = 142"
## [13] "Indices = 143" "Indices = 144"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 250" "Concs = 250" "Concs = 186.8824662"
## [4] "Concs = 208.9457498" "Concs = 167.0779465" "Concs = 229.5166359"
## [7] "Concs = 99.11335239" "Concs = 263.0350796" "Concs = 59.52448054"
## [10] "Concs = 46.29054385" "Concs = 51.98182232" "Concs = 162.0360626"
## [13] "Concs = 200.5560551" "Concs = 187.8908429"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 209.0664272 -0.9642375
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 85.2
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -104.92 -67.65 27.05 47.27 82.90
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 209.0664 31.6894 6.5974
## Time[ind] -0.9642 0.6045 -1.5951
##
## Residual standard error: 85.24 on 12 degrees of freedom
## (Intercept) Time[ind]
## 209.0664272 -0.9642375
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 10 obs. of 2 variables:
## $ sub: num 0.681 10 2.89 50 75 ...
## $ vel: num -16.7 -360.4 -71.9 -1039.2 -363.1 ...## sub vel
## 1 0.68082 -16.66194
## 2 10.00000 -360.42636
## 3 2.89000 -71.94424
## 4 50.00000 -1039.17744
## 5 75.00000 -363.05343
## 6 100.00000 -1625.77622
## 7 125.00000 -2414.36930
## 8 150.00000 -2107.58237
## 9 200.00000 7272.49406
## 10 250.00000 -4821.18755
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) -745.65932 1444.04137 -0.51637 0.6196
## e:(Intercept) 6.46479 70.23134 0.09205 0.9289
##
## Residual standard error:
##
## 3291.458 (8 degrees of freedom)
tdla
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 0.68"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.124349504" "Concs = 0.14627783" "Concs = 0.089752887"
## [7] "Concs = 0.107638677" "Concs = 0.159434476" "Concs = 0.159787554"
## [10] "Concs = 0.099828091" "Concs = 0.225228369" "Concs = 0.139329405"
## [13] "Concs = 0.072482112" "Concs = 0.09994686" "Concs = 0.061506341"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.0761456879 0.0005869689
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0909
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.076146 -0.061979 0.004803 0.050363 0.113865
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0761 0.0261 2.9175
## Time[ind] 0.0006 0.0005 1.1390
##
## Residual standard error: 0.09092 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.0761456879 0.0005869689
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.562008549" "Concs = 0.514503123" "Concs = 0.553400833"
## [7] "Concs = 0.914781067" "Concs = 0.896944628" "Concs = 0.854682343"
## [10] "Concs = 0.640465968" "Concs = 1.46510307" "Concs = 1.529173181"
## [13] "Concs = 1.670981262" "Concs = 1.594325825" "Concs = 1.598291535"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.20550710 0.01697908
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.27
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.58379 -0.17240 0.05431 0.16093 0.30492
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.2055 0.0914 2.2488
## Time[ind] 0.0170 0.0018 9.4097
##
## Residual standard error: 0.2699 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.20550710 0.01697908
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 31" "Indices = 32" "Indices = 33" "Indices = 34"
## [5] "Indices = 35" "Indices = 36" "Indices = 37" "Indices = 38"
## [9] "Indices = 39" "Indices = 40" "Indices = 41" "Indices = 42"
## [13] "Indices = 43" "Indices = 44"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.587769932" "Concs = 0.500911907" "Concs = 2.390614252"
## [7] "Concs = 0.732569141" "Concs = 0.819349521" "Concs = 0.882196657"
## [10] "Concs = 1.272480799" "Concs = 1.332879865" "Concs = 1.171215513"
## [13] "Concs = 1.284978616" "Concs = 1.466507839"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.24636291 0.01492835
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0.236
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.30494 -0.21562 0.03449 0.12910 1.92033
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.2464 0.0925 2.6647
## Time[ind] 0.0149 0.0020 7.5210
##
## Residual standard error: 0.236 on 12 degrees of freedom
## (Intercept) Time[ind]
## 0.24636291 0.01492835
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 45" "Indices = 46" "Indices = 47" "Indices = 48"
## [5] "Indices = 49" "Indices = 50" "Indices = 51" "Indices = 52"
## [9] "Indices = 53" "Indices = 54" "Indices = 55" "Indices = 56"
## [13] "Indices = 57" "Indices = 58" "Indices = 59"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 2.366202494" "Concs = 2.316676352" "Concs = 2.98040696"
## [7] "Concs = 2.746818134" "Concs = 3.431666105" "Concs = 3.294563534"
## [10] "Concs = 3.820882667" "Concs = 4.627112685" "Concs = 4.219456142"
## [13] "Concs = 4.7035697" "Concs = 4.419483485" "Concs = 4.677842802"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 1.16197557 0.04474367
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 1.14
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -1.1620 -0.6402 0.2425 0.6568 1.1473
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 1.1620 0.3417 3.4008
## Time[ind] 0.0447 0.0067 6.6322
##
## Residual standard error: 1.141 on 13 degrees of freedom
## (Intercept) Time[ind]
## 1.16197557 0.04474367
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 60" "Indices = 61" "Indices = 62" "Indices = 63"
## [5] "Indices = 64" "Indices = 65" "Indices = 66" "Indices = 67"
## [9] "Indices = 68" "Indices = 69" "Indices = 70" "Indices = 71"
## [13] "Indices = 72" "Indices = 73" "Indices = 74"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 2.219185884" "Concs = 2.155328801" "Concs = 2.202708256"
## [7] "Concs = 2.811019032" "Concs = 2.229132105" "Concs = 2.319209877"
## [10] "Concs = 3.438186485" "Concs = 3.239731804" "Concs = 3.112249253"
## [13] "Concs = 3.973569475" "Concs = 3.922150065" "Concs = 3.990347195"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 14 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 1.30612603 0.03145706
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.363
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -1.30613 -0.18940 -0.02071 0.31099 0.56118
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 1.3061 0.2061 6.3384
## Time[ind] 0.0315 0.0041 7.7313
##
## Residual standard error: 0.3627 on 13 degrees of freedom## (Intercept) Time[ind]
## 1.30612603 0.03145706
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 75" "Indices = 76" "Indices = 77" "Indices = 78"
## [5] "Indices = 79" "Indices = 80" "Indices = 81" "Indices = 82"
## [9] "Indices = 83" "Indices = 84" "Indices = 85" "Indices = 86"
## [13] "Indices = 87" "Indices = 88" "Indices = 89"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 2.973173898" "Concs = 4.278761105" "Concs = 5.203600328"
## [7] "Concs = 3.752087918" "Concs = 4.489689601" "Concs = 4.3820044"
## [10] "Concs = 4.18858056" "Concs = 4.787062374" "Concs = 4.819935077"
## [13] "Concs = 5.229225315" "Concs = 5.541134166" "Concs = 5.363637277"## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Ran 20 iterations without convergence
##
## Coefficients:
## (Intercept) Time[ind]
## 2.52347511 0.03490097
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.646
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -2.52348 -0.43214 -0.07382 0.50695 2.15661
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 2.5235 0.4925 5.1243
## Time[ind] 0.0349 0.0097 3.5893
##
## Residual standard error: 0.6461 on 13 degrees of freedom
## (Intercept) Time[ind]
## 2.52347511 0.03490097
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 90" "Indices = 91" "Indices = 92" "Indices = 93"
## [5] "Indices = 94" "Indices = 95" "Indices = 96" "Indices = 97"
## [9] "Indices = 98" "Indices = 99" "Indices = 100" "Indices = 101"
## [13] "Indices = 102" "Indices = 103" "Indices = 104"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 3.664975002" "Concs = 5.128116042" "Concs = 3.342678541"
## [7] "Concs = 3.909877303" "Concs = 3.131834777" "Concs = 6.184369077"
## [10] "Concs = 5.034115174" "Concs = 6.997125798" "Concs = 5.513028895"
## [13] "Concs = 5.609126979" "Concs = 6.565737598" "Concs = 6.051117386"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 1.7560769 0.0576901
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 1.55
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -1.7561 -1.1181 -0.1834 0.8824 2.6976
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 1.7561 0.6731 2.6090
## Time[ind] 0.0577 0.0133 4.3408
##
## Residual standard error: 1.547 on 13 degrees of freedom
## (Intercept) Time[ind]
## 1.7560769 0.0576901
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 105" "Indices = 106" "Indices = 107" "Indices = 108"
## [5] "Indices = 109" "Indices = 110" "Indices = 111" "Indices = 112"
## [9] "Indices = 113" "Indices = 114" "Indices = 115" "Indices = 116"
## [13] "Indices = 117" "Indices = 118" "Indices = 119"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 4.690841414" "Concs = 4.417155339" "Concs = 6.21277087"
## [7] "Concs = 3.839544319" "Concs = 4.519625245" "Concs = 6.760429619"
## [10] "Concs = 7.2240805" "Concs = 3.468203577" "Concs = 4.462789205"
## [13] "Concs = 8.035064896" "Concs = 8.748204845" "Concs = 7.504701282"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 2.03606128 0.06725212
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 2.38
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -2.60299 -1.82223 -0.05369 1.26260 3.16793
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 2.0361 0.7623 2.6708
## Time[ind] 0.0673 0.0151 4.4679
##
## Residual standard error: 2.385 on 13 degrees of freedom## (Intercept) Time[ind]
## 2.03606128 0.06725212
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 120" "Indices = 121" "Indices = 122" "Indices = 123"
## [5] "Indices = 124" "Indices = 125" "Indices = 126" "Indices = 127"
## [9] "Indices = 128" "Indices = 129" "Indices = 130"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 30"
## [6] "Times = 30" "Times = 60" "Times = 60" "Times = 60" "Times = 90"
## [11] "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 17.81066063"
## [4] "Concs = 14.08273374" "Concs = 20.76679639" "Concs = 16.9957259"
## [7] "Concs = 18.08230553" "Concs = 16.51635254" "Concs = 17.9065353"
## [10] "Concs = 19.61630031" "Concs = 17.39520371"## Warning in rlm.default(x, y, weights, method = method, wt.method =
## wt.method, : 'rlm' failed to converge in 20 steps
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Ran 20 iterations without convergence
##
## Coefficients:
## (Intercept) Time[ind]
## 10.8512483 0.1088307
##
## Degrees of freedom: 11 total; 9 residual
## Scale estimate: 4.31
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -10.8512 -2.1403 0.5254 2.2393 6.6506
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 10.8512 3.0214 3.5914
## Time[ind] 0.1088 0.0586 1.8574
##
## Residual standard error: 4.313 on 9 degrees of freedom
## (Intercept) Time[ind]
## 10.8512483 0.1088307
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 9 obs. of 2 variables:
## $ sub: num 0.68 10 2.89 50 75 100 125 150 250
## $ vel: num 2.93 84.9 74.64 223.72 157.29 ...## sub vel
## 1 0.68 2.934844
## 2 10.00 84.895393
## 3 2.89 74.641768
## 4 50.00 223.718355
## 5 75.00 157.285301
## 6 100.00 174.504835
## 7 125.00 288.450483
## 8 150.00 336.260615
## 9 250.00 544.153446
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 3163.18381 4980.22485 0.63515 0.5455
## e:(Intercept) 1238.39731 2229.91648 0.55536 0.5959
##
## Residual standard error:
##
## 57.11426 (7 degrees of freedom)
tdlb
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 0.68"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.159849035" "Concs = 0.171671782" "Concs = 0.137258352"
## [7] "Concs = 0.135498718" "Concs = 0.166579942" "Concs = 0.160555121"
## [10] "Concs = 0.085155894" "Concs = 0.137641779" "Concs = 0.101223849"
## [13] "Concs = 0.041122976" "Concs = 0.056120989" "Concs = 0.040770384"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 11 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.1007351193 -0.0001600198
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.069
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.10074 -0.04539 0.01009 0.05401 0.07334
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.1007 0.0339 2.9681
## Time[ind] -0.0002 0.0007 -0.2388
##
## Residual standard error: 0.06895 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.1007351193 -0.0001600198
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.540578005" "Concs = 0.535327972" "Concs = 0.549947891"
## [7] "Concs = 0.963906807" "Concs = 0.939249694" "Concs = 0.8832653"
## [10] "Concs = 0.462660817" "Concs = 1.424227752" "Concs = 1.466547242"
## [13] "Concs = 1.470094516" "Concs = 1.424845158" "Concs = 1.471282702"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 3 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.24121948 0.01487844
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.358
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.67126 -0.19833 0.07093 0.22368 0.33262
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.2412 0.1117 2.1597
## Time[ind] 0.0149 0.0022 6.7465
##
## Residual standard error: 0.3576 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.24121948 0.01487844
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 31" "Indices = 32" "Indices = 33" "Indices = 34"
## [5] "Indices = 35" "Indices = 36" "Indices = 37" "Indices = 38"
## [9] "Indices = 39" "Indices = 40" "Indices = 41" "Indices = 42"
## [13] "Indices = 43" "Indices = 44" "Indices = 45"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.502687773" "Concs = 0.443748362" "Concs = 1.739413295"
## [7] "Concs = 0.631006803" "Concs = 0.676925019" "Concs = 0.712219102"
## [10] "Concs = 0.887492395" "Concs = 0.922424215" "Concs = 0.774293903"
## [13] "Concs = 0.733501521" "Concs = 0.837366651" "Concs = 0.76078022"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.294045960 0.007259556
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.277
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.29405 -0.20027 0.04467 0.16148 1.33647
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.2940 0.0978 3.0069
## Time[ind] 0.0073 0.0019 3.7597
##
## Residual standard error: 0.2767 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.294045960 0.007259556
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 46" "Indices = 47" "Indices = 48" "Indices = 49"
## [5] "Indices = 50" "Indices = 51" "Indices = 52" "Indices = 53"
## [9] "Indices = 54" "Indices = 55" "Indices = 56" "Indices = 57"
## [13] "Indices = 58" "Indices = 59" "Indices = 60"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 2.598887073" "Concs = 2.355603277" "Concs = 3.141649164"
## [7] "Concs = 3.674320887" "Concs = 4.289723095" "Concs = 4.280136564"
## [10] "Concs = 6.243599629" "Concs = 6.734010485" "Concs = 6.361017452"
## [13] "Concs = 7.195467955" "Concs = 6.834134189" "Concs = 6.9532999"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 1.12601129 0.07482339
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 1.34
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -1.1260 -0.9664 0.3036 0.8194 1.1186
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 1.1260 0.3726 3.0221
## Time[ind] 0.0748 0.0074 10.1706
##
## Residual standard error: 1.344 on 13 degrees of freedom
## (Intercept) Time[ind]
## 1.12601129 0.07482339
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 61" "Indices = 62" "Indices = 63" "Indices = 64"
## [5] "Indices = 65" "Indices = 66" "Indices = 67" "Indices = 68"
## [9] "Indices = 69" "Indices = 70" "Indices = 71" "Indices = 72"
## [13] "Indices = 73" "Indices = 74" "Indices = 75"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 2.526757358" "Concs = 2.313637237" "Concs = 2.49086012"
## [7] "Concs = 3.789628052" "Concs = 3.174642429" "Concs = 3.191438558"
## [10] "Concs = 5.432233942" "Concs = 4.969157891" "Concs = 5.064503301"
## [13] "Concs = 6.712664257" "Concs = 6.597464296" "Concs = 6.484914"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.85929819 0.06813407
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.719
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.8593 -0.4502 0.1172 0.4586 0.8863
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.8593 0.2477 3.4686
## Time[ind] 0.0681 0.0049 13.9290
##
## Residual standard error: 0.7189 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.85929819 0.06813407
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 76" "Indices = 77" "Indices = 78" "Indices = 79"
## [5] "Indices = 80" "Indices = 81" "Indices = 82" "Indices = 83"
## [9] "Indices = 84" "Indices = 85" "Indices = 86" "Indices = 87"
## [13] "Indices = 88" "Indices = 89" "Indices = 90"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 2.987986855" "Concs = 4.62322369" "Concs = 5.738654903"
## [7] "Concs = 5.010985215" "Concs = 6.920302664" "Concs = 6.308852644"
## [10] "Concs = 8.11715413" "Concs = 8.804687457" "Concs = 8.950282552"
## [13] "Concs = 10.81651263" "Concs = 11.45788264" "Concs = 11.01782631"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 1.6091805 0.1129751
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 1.42
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -1.6092 -0.8598 -0.2705 0.9365 2.4348
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 1.6092 0.6040 2.6640
## Time[ind] 0.1130 0.0119 9.4723
##
## Residual standard error: 1.424 on 13 degrees of freedom
## (Intercept) Time[ind]
## 1.6091805 0.1129751
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 91" "Indices = 92" "Indices = 93" "Indices = 94"
## [5] "Indices = 95" "Indices = 96" "Indices = 97" "Indices = 98"
## [9] "Indices = 99" "Indices = 100" "Indices = 101" "Indices = 102"
## [13] "Indices = 103" "Indices = 104" "Indices = 105"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 4.759629498" "Concs = 6.081131385" "Concs = 4.761075887"
## [7] "Concs = 6.970865526" "Concs = 5.864292522" "Concs = 8.990170569"
## [10] "Concs = 10.29254833" "Concs = 11.89986315" "Concs = 10.55439287"
## [13] "Concs = 12.66145718" "Concs = 13.84087365" "Concs = 12.77355717"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 3 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 2.0103474 0.1354138
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 2.11
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -2.0103 -1.4801 0.1574 0.8088 2.9174
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 2.0103 0.7091 2.8353
## Time[ind] 0.1354 0.0140 9.6723
##
## Residual standard error: 2.111 on 13 degrees of freedom
## (Intercept) Time[ind]
## 2.0103474 0.1354138
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 106" "Indices = 107" "Indices = 108" "Indices = 109"
## [5] "Indices = 110" "Indices = 111" "Indices = 112" "Indices = 113"
## [9] "Indices = 114" "Indices = 115" "Indices = 116" "Indices = 117"
## [13] "Indices = 118" "Indices = 119" "Indices = 120"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 6.090475637" "Concs = 5.80525893" "Concs = 8.98551562"
## [7] "Concs = 6.941039356" "Concs = 7.206821805" "Concs = 10.94796175"
## [10] "Concs = 13.80091931" "Concs = 7.457397291" "Concs = 9.668427529"
## [13] "Concs = 16.81467648" "Concs = 18.96446187" "Concs = 16.539466"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 2.0306945 0.1686676
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 2.6
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -4.6934 -2.0307 -0.1497 1.5900 4.4248
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 2.0307 1.1765 1.7260
## Time[ind] 0.1687 0.0232 7.2605
##
## Residual standard error: 2.6 on 13 degrees of freedom
## (Intercept) Time[ind]
## 2.0306945 0.1686676
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 121" "Indices = 122" "Indices = 123" "Indices = 124"
## [5] "Indices = 125" "Indices = 126" "Indices = 127" "Indices = 128"
## [9] "Indices = 129" "Indices = 130" "Indices = 131"
## [1] "Times = 0" "Times = 0" "Times = 15" "Times = 15" "Times = 30"
## [6] "Times = 30" "Times = 60" "Times = 60" "Times = 60" "Times = 90"
## [11] "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 22.19280552"
## [4] "Concs = 17.62020275" "Concs = 24.15778887" "Concs = 20.49970666"
## [7] "Concs = 25.33183553" "Concs = 23.63873667" "Concs = 25.85088774"
## [10] "Concs = 28.34728168" "Concs = 25.77673742"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 18 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 14.9606591 0.1539254
##
## Degrees of freedom: 11 total; 9 residual
## Scale estimate: 2.45
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -14.9607 -1.7973 0.3507 1.3952 4.9233
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 14.9607 2.2073 6.7778
## Time[ind] 0.1539 0.0428 3.5960
##
## Residual standard error: 2.453 on 9 degrees of freedom
## (Intercept) Time[ind]
## 14.9606591 0.1539254
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 9 obs. of 2 variables:
## $ sub: num 0.68 10 2.89 50 75 100 125 150 250
## $ vel: num -0.8 74.4 36.3 374.1 340.7 ...## sub vel
## 1 0.68 -0.8000989
## 2 10.00 74.3921896
## 3 2.89 36.2977812
## 4 50.00 374.1169252
## 5 75.00 340.6703300
## 6 100.00 564.8754297
## 7 125.00 677.0688071
## 8 150.00 843.3378548
## 9 250.00 769.6270565
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 1299.5681 282.4222 4.6015 0.0025
## e:(Intercept) 130.7062 57.0056 2.2929 0.0556
##
## Residual standard error:
##
## 83.93925 (7 degrees of freedom)
fipronil
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 30" "Times = 30" "Times = 30" "Times = 60" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 10" "Concs = 10" "Concs = 10"
## [4] "Concs = 7.601993848" "Concs = 11.87171779" "Concs = 8.347482218"
## [7] "Concs = 12.54233702" "Concs = 9.213313367" "Concs = 10.38856477"
## [10] "Concs = 12.36949156" "Concs = 8.215365646" "Concs = 11.17931895"
## [13] "Concs = 12.71923746" "Concs = 9.99477721"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 9.7136033 0.0148301
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 2.02
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -2.3880 -1.0264 0.2087 1.3248 2.3838
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 9.7136 0.6968 13.9394
## Time[ind] 0.0148 0.0133 1.1124
##
## Residual standard error: 2.02 on 12 degrees of freedom
## (Intercept) Time[ind]
## 9.7136033 0.0148301
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 15" "Indices = 16" "Indices = 17" "Indices = 18"
## [5] "Indices = 19" "Indices = 20" "Indices = 21" "Indices = 22"
## [9] "Indices = 23" "Indices = 24" "Indices = 25" "Indices = 26"
## [13] "Indices = 27" "Indices = 28" "Indices = 29"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 2.89" "Concs = 2.89" "Concs = 2.89"
## [4] "Concs = 0.961731316" "Concs = 0.608701865" "Concs = 2.021395291"
## [7] "Concs = 0.34095865" "Concs = 1.416552854" "Concs = 4.678731136"
## [10] "Concs = 1.597568113" "Concs = 2.059112975" "Concs = 4.336224939"
## [13] "Concs = 0.73593197" "Concs = 1.01143428" "Concs = 2.098949857"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 7 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 2.239880567 -0.009035236
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.964
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -1.62786 -0.62152 -0.08296 0.65012 2.70991
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 2.2399 0.5303 4.2238
## Time[ind] -0.0090 0.0105 -0.8629
##
## Residual standard error: 0.9636 on 13 degrees of freedom
## (Intercept) Time[ind]
## 2.239880567 -0.009035236
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 30" "Indices = 31" "Indices = 32" "Indices = 33"
## [5] "Indices = 34" "Indices = 35" "Indices = 36" "Indices = 37"
## [9] "Indices = 38" "Indices = 39" "Indices = 40" "Indices = 41"
## [13] "Indices = 42" "Indices = 43" "Indices = 44"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 50" "Concs = 50" "Concs = 50"
## [4] "Concs = 223.3849191" "Concs = 19.09530124" "Concs = 61.85004879"
## [7] "Concs = 76.72890033" "Concs = 65.4447593" "Concs = 59.88633813"
## [10] "Concs = 74.09066447" "Concs = 65.54242812" "Concs = 39.55208359"
## [13] "Concs = 66.15498564" "Concs = 23.55175796" "Concs = 58.25965938"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 10 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 56.75972024 0.05173236
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 10
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -38.440 -6.760 1.575 6.406 165.849
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 56.7597 7.5676 7.5003
## Time[ind] 0.0517 0.1494 0.3462
##
## Residual standard error: 10.02 on 13 degrees of freedom
## (Intercept) Time[ind]
## 56.75972024 0.05173236
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 45" "Indices = 46" "Indices = 47" "Indices = 48"
## [5] "Indices = 49" "Indices = 50" "Indices = 51" "Indices = 52"
## [9] "Indices = 53" "Indices = 54" "Indices = 55" "Indices = 56"
## [13] "Indices = 57" "Indices = 58"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 75" "Concs = 75" "Concs = 75"
## [4] "Concs = 35.05455395" "Concs = 40.30349338" "Concs = 44.1381674"
## [7] "Concs = 38.08049817" "Concs = 38.34527612" "Concs = 89.31881211"
## [10] "Concs = 40.27279664" "Concs = 55.95173867" "Concs = 37.82415225"
## [13] "Concs = 32.32010713" "Concs = 45.93427684"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 61.0033064 -0.2664754
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 20.8
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -21.952 -14.215 -1.948 13.232 36.310
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 61.0033 6.9492 8.7785
## Time[ind] -0.2665 0.1392 -1.9139
##
## Residual standard error: 20.75 on 12 degrees of freedom
## (Intercept) Time[ind]
## 61.0033064 -0.2664754
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 59" "Indices = 60" "Indices = 61" "Indices = 62"
## [5] "Indices = 63" "Indices = 64" "Indices = 65" "Indices = 66"
## [9] "Indices = 67" "Indices = 68" "Indices = 69" "Indices = 70"
## [13] "Indices = 71" "Indices = 72" "Indices = 73"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 100" "Concs = 100" "Concs = 100"
## [4] "Concs = 65.75118371" "Concs = 61.03836189" "Concs = 86.42270417"
## [7] "Concs = 18.77293974" "Concs = 84.04356305" "Concs = 89.30314297"
## [10] "Concs = 60.95565287" "Concs = 89.79580177" "Concs = 90.59062961"
## [13] "Concs = 56.03613412" "Concs = 94.58659729" "Concs = 89.70085579"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 85.20373140 -0.09753929
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 21.9
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -63.505 -18.193 7.026 14.036 18.161
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 85.2037 7.6083 11.1988
## Time[ind] -0.0975 0.1502 -0.6493
##
## Residual standard error: 21.94 on 13 degrees of freedom
## (Intercept) Time[ind]
## 85.20373140 -0.09753929
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 74" "Indices = 75" "Indices = 76" "Indices = 77"
## [5] "Indices = 78" "Indices = 79" "Indices = 80" "Indices = 81"
## [9] "Indices = 82" "Indices = 83" "Indices = 84" "Indices = 85"
## [13] "Indices = 86" "Indices = 87" "Indices = 88"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 125" "Concs = 125" "Concs = 125"
## [4] "Concs = 62.24891641" "Concs = 54.68420677" "Concs = 91.10795719"
## [7] "Concs = 51.66702524" "Concs = 65.6950903" "Concs = 112.1237445"
## [10] "Concs = 62.81350539" "Concs = 74.14828799" "Concs = 93.87631612"
## [13] "Concs = 59.80299767" "Concs = 82.33654045" "Concs = 89.20514072"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 97.525349 -0.321659
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 32.9
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -38.016 -18.796 -1.593 22.439 27.475
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 97.5253 10.1778 9.5821
## Time[ind] -0.3217 0.2010 -1.6006
##
## Residual standard error: 32.88 on 13 degrees of freedom
## (Intercept) Time[ind]
## 97.525349 -0.321659
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 89" "Indices = 90" "Indices = 91" "Indices = 92"
## [5] "Indices = 93" "Indices = 94" "Indices = 95" "Indices = 96"
## [9] "Indices = 97" "Indices = 98" "Indices = 99" "Indices = 100"
## [13] "Indices = 101" "Indices = 102" "Indices = 103"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 150" "Concs = 150" "Concs = 150"
## [4] "Concs = 37.15191594" "Concs = 76.95257401" "Concs = 82.83018255"
## [7] "Concs = 89.28298886" "Concs = 103.9076465" "Concs = 88.89209516"
## [10] "Concs = 75.20034761" "Concs = 99.21349783" "Concs = 86.10641447"
## [13] "Concs = 85.35534061" "Concs = 86.89358929" "Concs = 19.45762438"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 4 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 118.4201583 -0.6413674
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 38.5
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -71.648 -18.128 4.729 25.427 31.580
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 118.4202 12.7515 9.2868
## Time[ind] -0.6414 0.2518 -2.5474
##
## Residual standard error: 38.51 on 13 degrees of freedom
## (Intercept) Time[ind]
## 118.4201583 -0.6413674
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 200"
## [1] "Indices = 104" "Indices = 105" "Indices = 106" "Indices = 107"
## [5] "Indices = 108" "Indices = 109" "Indices = 110" "Indices = 111"
## [9] "Indices = 112" "Indices = 113" "Indices = 114" "Indices = 115"
## [13] "Indices = 116" "Indices = 117" "Indices = 118"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 200" "Concs = 200" "Concs = 200"
## [4] "Concs = 143.5820327" "Concs = 117.0381728" "Concs = 105.3992543"
## [7] "Concs = 120.601107" "Concs = 115.1379412" "Concs = 126.1830373"
## [10] "Concs = 91.91948648" "Concs = 106.6462813" "Concs = 72.50149496"
## [13] "Concs = 112.4063583" "Concs = 105.3992543" "Concs = 111.7531537"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 160.8018480 -0.8264276
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 37.6
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -43.006 -20.084 -4.823 25.656 39.198
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 160.8018 12.1956 13.1853
## Time[ind] -0.8264 0.2408 -3.4320
##
## Residual standard error: 37.55 on 13 degrees of freedom
## (Intercept) Time[ind]
## 160.8018480 -0.8264276
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 119" "Indices = 120" "Indices = 121" "Indices = 122"
## [5] "Indices = 123" "Indices = 124" "Indices = 125" "Indices = 126"
## [9] "Indices = 127" "Indices = 128" "Indices = 129" "Indices = 130"
## [13] "Indices = 131" "Indices = 132" "Indices = 133"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 250" "Concs = 250" "Concs = 250"
## [4] "Concs = 105.2844752" "Concs = 83.9166222" "Concs = 57.25407999"
## [7] "Concs = 71.31021926" "Concs = 93.93871253" "Concs = 36.95777127"
## [10] "Concs = 77.4873567" "Concs = 101.3134582" "Concs = 91.54349597"
## [13] "Concs = 58.38865626" "Concs = 74.14665992" "Concs = 61.1620649"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 13 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 130.535247 -0.826428
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 30.2
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -68.785 -23.538 2.232 19.177 119.465
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 130.5352 19.5920 6.6627
## Time[ind] -0.8264 0.3868 -2.1363
##
## Residual standard error: 30.18 on 13 degrees of freedom
## (Intercept) Time[ind]
## 130.535247 -0.826428
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 9 obs. of 2 variables:
## $ sub: num 10 2.89 50 75 100 125 150 200 250
## $ vel: num 74.2 -45.2 258.7 -1332.4 -487.7 ...## sub vel
## 1 10.00 74.15048
## 2 2.89 -45.17618
## 3 50.00 258.66179
## 4 75.00 -1332.37704
## 5 100.00 -487.69647
## 6 125.00 -1608.29494
## 7 150.00 -3206.83717
## 8 200.00 -4132.13800
## 9 250.00 -4132.13998
## Warning in sqrt(diag(varMat)): NaNs produced##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) -12885044 NA NA NA
## e:(Intercept) 764537 0 Inf 0
##
## Residual standard error:
##
## 756.617 (7 degrees of freedom)## Warning in sqrt(diag(varMat)): NaNs produced
fipsulf
The above figure shows a three-dimensional plot of pesticide substrate concentration, observed concentration and experiment time. We need to condition the pesticide data on the substrate concentrations used in the experiment and regress the observed concentrations over the 90 min period in order to estimate the linear slopes for the Michaelis-Menten kinetic rate constants.
## [1] "Substrates:"## [1] "##################################################"
## [1] "Substrate = 10"
## [1] "Indices = 1" "Indices = 2" "Indices = 3" "Indices = 4"
## [5] "Indices = 5" "Indices = 6" "Indices = 7" "Indices = 8"
## [9] "Indices = 9" "Indices = 10" "Indices = 11" "Indices = 12"
## [13] "Indices = 13" "Indices = 14" "Indices = 15"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.226052779" "Concs = 0.249546426" "Concs = 0.249495111"
## [7] "Concs = 0.556306401" "Concs = 0.629523416" "Concs = 0.545734442"
## [10] "Concs = 1.029532274" "Concs = 1.020828782" "Concs = 1.121529265"
## [13] "Concs = 1.478049545" "Concs = 1.552223152" "Concs = 1.605171177"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 5 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.002836538 0.017390372
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.0314
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.089920 -0.016237 -0.002837 0.026473 0.104976
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0028 0.0154 0.1843
## Time[ind] 0.0174 0.0003 57.2338
##
## Residual standard error: 0.03141 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.002836538 0.017390372
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 2.89"
## [1] "Indices = 16" "Indices = 17" "Indices = 18" "Indices = 19"
## [5] "Indices = 20" "Indices = 21" "Indices = 22" "Indices = 23"
## [9] "Indices = 24" "Indices = 25" "Indices = 26" "Indices = 27"
## [13] "Indices = 28" "Indices = 29" "Indices = 30"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0" "Concs = 0" "Concs = 0"
## [7] "Concs = 0.072417652" "Concs = 0.105189206" "Concs = 0.093830232"
## [10] "Concs = 0.446059868" "Concs = 0.501873862" "Concs = 1.937676963"
## [13] "Concs = 0.541481009" "Concs = 0.713021528" "Concs = 0.948269563"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 11 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## -0.083977895 0.009007886
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.125
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.18525 -0.06610 -0.01371 0.08398 1.48118
##
## Coefficients:
## Value Std. Error t value
## (Intercept) -0.0840 0.0551 -1.5251
## Time[ind] 0.0090 0.0011 8.2849
##
## Residual standard error: 0.1245 on 13 degrees of freedom
## (Intercept) Time[ind]
## -0.083977895 0.009007886
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 50"
## [1] "Indices = 31" "Indices = 32" "Indices = 33" "Indices = 34"
## [5] "Indices = 35" "Indices = 36" "Indices = 37" "Indices = 38"
## [9] "Indices = 39" "Indices = 40" "Indices = 41" "Indices = 42"
## [13] "Indices = 43" "Indices = 44" "Indices = 45"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 2.509901494" "Concs = 0.497072024" "Concs = 0.573048602"
## [7] "Concs = 0.208702278" "Concs = 1.224307072" "Concs = 0.86186791"
## [10] "Concs = 2.640613398" "Concs = 2.278728642" "Concs = 1.938091721"
## [13] "Concs = 3.288556396" "Concs = 2.79424236" "Concs = 2.85277407"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 6 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.05707229 0.03336470
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.291
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.84931 -0.15850 -0.05707 0.19303 1.95236
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.0571 0.1273 0.4483
## Time[ind] 0.0334 0.0025 13.2724
##
## Residual standard error: 0.2908 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.05707229 0.03336470
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 75"
## [1] "Indices = 46" "Indices = 47" "Indices = 48" "Indices = 49"
## [5] "Indices = 50" "Indices = 51" "Indices = 52" "Indices = 53"
## [9] "Indices = 54" "Indices = 55" "Indices = 56" "Indices = 57"
## [13] "Indices = 58" "Indices = 59"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.61596018" "Concs = 0.004496637" "Concs = 0.393574273"
## [7] "Concs = 1.00896852" "Concs = 1.080335369" "Concs = 1.122428808"
## [10] "Concs = 0.794034486" "Concs = 1.567175192" "Concs = 1.445091993"
## [13] "Concs = 1.567376573" "Concs = 1.397216044"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 10 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.19229663 0.01558037
##
## Degrees of freedom: 14 total; 12 residual
## Scale estimate: 0.289
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.42151 -0.19230 -0.09093 0.30944 0.46272
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.1923 0.1778 1.0818
## Time[ind] 0.0156 0.0036 4.3745
##
## Residual standard error: 0.2889 on 12 degrees of freedom
## (Intercept) Time[ind]
## 0.19229663 0.01558037
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 100"
## [1] "Indices = 60" "Indices = 61" "Indices = 62" "Indices = 63"
## [5] "Indices = 64" "Indices = 65" "Indices = 66" "Indices = 67"
## [9] "Indices = 68" "Indices = 69" "Indices = 70" "Indices = 71"
## [13] "Indices = 72" "Indices = 73" "Indices = 74"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 1.037370756" "Concs = 1.004548869" "Concs = 1.211451943"
## [7] "Concs = 1.770038982" "Concs = 1.964421756" "Concs = 2.082784287"
## [10] "Concs = 2.421230649" "Concs = 2.716290502" "Concs = 2.511880669"
## [13] "Concs = 2.884476336" "Concs = 3.658963096" "Concs = 3.101044324"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 2 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.45728114 0.03333895
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.463
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.57331 -0.40701 0.05426 0.25638 0.62533
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.4573 0.1723 2.6539
## Time[ind] 0.0333 0.0034 9.7994
##
## Residual standard error: 0.4635 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.45728114 0.03333895
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 125"
## [1] "Indices = 75" "Indices = 76" "Indices = 77" "Indices = 78"
## [5] "Indices = 79" "Indices = 80" "Indices = 81" "Indices = 82"
## [9] "Indices = 83" "Indices = 84" "Indices = 85" "Indices = 86"
## [13] "Indices = 87" "Indices = 88" "Indices = 89"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 1.0685532" "Concs = 1.193964217" "Concs = 1.061157254"
## [7] "Concs = 1.739690158" "Concs = 1.568026457" "Concs = 1.831902381"
## [10] "Concs = 2.58185903" "Concs = 2.518118409" "Concs = 2.706182414"
## [13] "Concs = 3.388713261" "Concs = 3.265199632" "Concs = 3.360717697"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.38590066 0.03503517
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.323
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.38590 -0.22611 0.09385 0.18765 0.39495
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.3859 0.1137 3.3954
## Time[ind] 0.0350 0.0022 15.6121
##
## Residual standard error: 0.3235 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.38590066 0.03503517
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 150"
## [1] "Indices = 90" "Indices = 91" "Indices = 92" "Indices = 93"
## [5] "Indices = 94" "Indices = 95" "Indices = 96" "Indices = 97"
## [9] "Indices = 98" "Indices = 99" "Indices = 100" "Indices = 101"
## [13] "Indices = 102" "Indices = 103" "Indices = 104"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 1.513101462" "Concs = 1.254618226" "Concs = 1.316915121"
## [7] "Concs = 1.847166036" "Concs = 2.06265471" "Concs = 2.225655093"
## [10] "Concs = 3.029089226" "Concs = 2.818619179" "Concs = 2.892261352"
## [13] "Concs = 3.395108251" "Concs = 3.493680617" "Concs = 3.346621743"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.57091928 0.03526787
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.519
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.5709 -0.3742 0.1547 0.2802 0.5967
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.5709 0.1714 3.3306
## Time[ind] 0.0353 0.0034 10.4200
##
## Residual standard error: 0.5188 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.57091928 0.03526787
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 200"
## [1] "Indices = 105" "Indices = 106" "Indices = 107" "Indices = 108"
## [5] "Indices = 109" "Indices = 110" "Indices = 111" "Indices = 112"
## [9] "Indices = 113" "Indices = 114" "Indices = 115" "Indices = 116"
## [13] "Indices = 117" "Indices = 118" "Indices = 119"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.921840151" "Concs = 1.265455207" "Concs = 0.083794693"
## [7] "Concs = 1.758009212" "Concs = 1.131761977" "Concs = 2.14032494"
## [10] "Concs = 3.119569212" "Concs = 5.219960219" "Concs = 3.68483357"
## [13] "Concs = 4.382618411" "Concs = 4.121095689" "Concs = 4.42249183"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 8 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.13348422 0.04865162
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.245
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.77946 -0.13348 -0.08964 0.28359 2.16738
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.1335 0.2209 0.6041
## Time[ind] 0.0487 0.0044 11.1519
##
## Residual standard error: 0.2446 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.13348422 0.04865162
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"
## [1] "##################################################"
## [1] "Substrate = 250"
## [1] "Indices = 120" "Indices = 121" "Indices = 122" "Indices = 123"
## [5] "Indices = 124" "Indices = 125" "Indices = 126" "Indices = 127"
## [9] "Indices = 128" "Indices = 129" "Indices = 130" "Indices = 131"
## [13] "Indices = 132" "Indices = 133" "Indices = 134"
## [1] "Times = 0" "Times = 0" "Times = 0" "Times = 15" "Times = 15"
## [6] "Times = 15" "Times = 30" "Times = 30" "Times = 30" "Times = 60"
## [11] "Times = 60" "Times = 60" "Times = 90" "Times = 90" "Times = 90"
## [1] "Concs = 0" "Concs = 0" "Concs = 0"
## [4] "Concs = 0.688691412" "Concs = 0.680203691" "Concs = 0.671715969"
## [7] "Concs = 1.128032043" "Concs = 1.057705208" "Concs = 1.0791266"
## [10] "Concs = 1.670842039" "Concs = 1.655483305" "Concs = 1.672054571"
## [13] "Concs = 2.11584115" "Concs = 2.394723427" "Concs = 2.276703681"
## Call:
## rlm(formula = Observed[ind] ~ Time[ind])
## Converged in 1 iterations
##
## Coefficients:
## (Intercept) Time[ind]
## 0.21108314 0.02380321
##
## Degrees of freedom: 15 total; 13 residual
## Scale estimate: 0.179
##
## Call: rlm(formula = Observed[ind] ~ Time[ind])
## Residuals:
## Min 1Q Median 3Q Max
## -0.23753 -0.14388 0.03278 0.11632 0.20285
##
## Coefficients:
## Value Std. Error t value
## (Intercept) 0.2111 0.0635 3.3230
## Time[ind] 0.0238 0.0013 18.9784
##
## Residual standard error: 0.1787 on 13 degrees of freedom
## (Intercept) Time[ind]
## 0.21108314 0.02380321
## 2.5 % 97.5 %
## (Intercept) NA NA
## Time[ind] NA NA
## [1] "##################################################"## 'data.frame': 9 obs. of 2 variables:
## $ sub: num 10 2.89 50 75 100 125 150 200 250
## $ vel: num 87 45 166.8 77.9 166.7 ...## sub vel
## 1 10.00 86.95186
## 2 2.89 45.03943
## 3 50.00 166.82351
## 4 75.00 77.90185
## 5 100.00 166.69476
## 6 125.00 175.17585
## 7 150.00 176.33933
## 8 200.00 243.25811
## 9 250.00 119.01603
##
## Model fitted: Michaelis-Menten (2 parms)
##
## Parameter estimates:
##
## Estimate Std. Error t-value p-value
## d:(Intercept) 177.90201 27.92410 6.37091 0.0004
## e:(Intercept) 10.95581 11.57501 0.94651 0.3754
##
## Residual standard error:
##
## 46.2558 (7 degrees of freedom)
exposure experiment analysis
Results presentation and discussion for parent analytes (atrazine, triadimenon, and fipronil) and their xenobiotic metabolites.
Toxicity of parents and metabolites discussion.
Microsomal analysis of soil and amphibian data for 0 (soil only), 2, 4, 12, 24, and 48 hours after exposure.
Database has factors for time, parent (mapped to analyte), analyte (can be either parent or metabolite), matrix (amphibian or soil), and tank (potentially a nuisance variable).
## Classes 'grouped_df', 'tbl_df', 'tbl' and 'data.frame': 352 obs. of 6 variables:
## $ time : int 2 2 2 2 4 4 4 4 12 12 ...
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 1 1 1 1 1 ...
## $ conc : num 3.07 3.69 4.7 1.89 7.62 ...
## $ replicate: Factor w/ 4 levels "1","2","3","4": 1 2 3 4 1 2 3 4 1 2 ...
## - attr(*, "vars")=List of 4
## ..$ : symbol parent
## ..$ : symbol analyte
## ..$ : symbol matrix
## ..$ : symbol time
## - attr(*, "drop")= logi TRUE
## - attr(*, "indices")=List of 86
## ..$ : int 0 1 2 3
## ..$ : int 4 5 6 7
## ..$ : int 8 9 10 11
## ..$ : int 12 13 14 15
## ..$ : int 16 17 18 19
## ..$ : int 20 21 22 23
## ..$ : int 24 25 26 27
## ..$ : int 28 29 30 31
## ..$ : int 32 33 34 35
## ..$ : int 36 37 38 39
## ..$ : int 40 41 42 43
## ..$ : int 88 89 90 91
## ..$ : int 92 93 94 95
## ..$ : int 96 97 98 99
## ..$ : int 100 101 102 103
## ..$ : int 104 105 106 107
## ..$ : int 108 109 110 111
## ..$ : int 112 113 114 115
## ..$ : int 116 117 118 119
## ..$ : int 120 121 122 123
## ..$ : int 124 125 126 127
## ..$ : int 128 129 130 131
## ..$ : int 44 45 46 47
## ..$ : int 48 49 50 51
## ..$ : int 52 53 54 55
## ..$ : int 56 57 58 59
## ..$ : int 60 61 62 63
## ..$ : int 64 65 66 67
## ..$ : int 68 69 70 71
## ..$ : int 72 73 74 75
## ..$ : int 76 77 78 79
## ..$ : int 80 81 82 83
## ..$ : int 84 85 86 87
## ..$ : int 264 265 266 267
## ..$ : int 268 269 270 271
## ..$ : int 272 273 274 275
## ..$ : int 276 277 278 279
## ..$ : int 280 281 282 283
## ..$ : int 284 285 286 287 288 289 290 291
## ..$ : int 292 293 294 295
## ..$ : int 296 297 298 299
## ..$ : int 300 301 302 303
## ..$ : int 304 305 306 307
## ..$ : int 308 309 310 311
## ..$ : int 312 313 314 315
## ..$ : int 316 317 318 319
## ..$ : int 320 321 322 323
## ..$ : int 324 325 326 327
## ..$ : int 328 329 330 331 332 333 334 335
## ..$ : int 336 337 338 339
## ..$ : int 340 341 342 343
## ..$ : int 344 345 346 347
## ..$ : int 348 349 350 351
## ..$ : int 176 177 178 179
## ..$ : int 180 181 182 183
## ..$ : int 184 185 186 187
## ..$ : int 188 189 190 191
## ..$ : int 192 193 194 195
## ..$ : int 196 197 198 199
## ..$ : int 200 201 202 203
## ..$ : int 204 205 206 207
## ..$ : int 208 209 210 211
## ..$ : int 212 213 214 215
## ..$ : int 216 217 218 219
## ..$ : int 220 221 222 223
## ..$ : int 224 225 226 227
## ..$ : int 228 229 230 231
## ..$ : int 232 233 234 235
## ..$ : int 236 237 238 239
## ..$ : int 240 241 242 243
## ..$ : int 244 245 246 247
## ..$ : int 248 249 250 251
## ..$ : int 252 253 254 255
## ..$ : int 256 257 258 259
## ..$ : int 260 261 262 263
## ..$ : int 132 133 134 135
## ..$ : int 136 137 138 139
## ..$ : int 140 141 142 143
## ..$ : int 144 145 146 147
## ..$ : int 148 149 150 151
## ..$ : int 152 153 154 155
## ..$ : int 156 157 158 159
## ..$ : int 160 161 162 163
## ..$ : int 164 165 166 167
## ..$ : int 168 169 170 171
## ..$ : int 172 173 174 175
## - attr(*, "group_sizes")= int 4 4 4 4 4 4 4 4 4 4 ...
## - attr(*, "biggest_group_size")= int 8
## - attr(*, "labels")='data.frame': 86 obs. of 4 variables:
## ..$ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## ..$ analyte: Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
## ..$ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 2 2 2 2 2 ...
## ..$ time : int 2 4 12 24 48 0 2 4 12 24 ...
## ..- attr(*, "vars")=List of 4
## .. ..$ : symbol parent
## .. ..$ : symbol analyte
## .. ..$ : symbol matrix
## .. ..$ : symbol time
## ..- attr(*, "drop")= logi TRUE## Source: local data frame [352 x 6]
## Groups: parent, analyte, matrix, time [86]
##
## time parent analyte matrix conc replicate
## (int) (fctr) (fctr) (fctr) (dbl) (fctr)
## 1 2 atrazine atrazine amphib 3.068203 1
## 2 2 atrazine atrazine amphib 3.689640 2
## 3 2 atrazine atrazine amphib 4.701166 3
## 4 2 atrazine atrazine amphib 1.892494 4
## 5 4 atrazine atrazine amphib 7.624610 1
## 6 4 atrazine atrazine amphib 4.134300 2
## 7 4 atrazine atrazine amphib 2.050779 3
## 8 4 atrazine atrazine amphib 7.626486 4
## 9 12 atrazine atrazine amphib 2.452278 1
## 10 12 atrazine atrazine amphib 3.786893 2
## .. ... ... ... ... ... ...## Source: local data frame [86 x 7]
## Groups: parent, analyte, matrix [?]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 atrazine atrazine amphib 2 4 3.337876 1.1753225
## 2 atrazine atrazine amphib 4 4 5.359044 2.7518903
## 3 atrazine atrazine amphib 12 4 3.123811 1.2566289
## 4 atrazine atrazine amphib 24 4 1.554919 0.6096102
## 5 atrazine atrazine amphib 48 4 1.001887 0.3545473
## 6 atrazine atrazine soil 0 4 15.930920 2.5911041
## 7 atrazine atrazine soil 2 4 19.029034 4.3534303
## 8 atrazine atrazine soil 4 4 18.770091 2.6953158
## 9 atrazine atrazine soil 12 4 20.614190 3.8918511
## 10 atrazine atrazine soil 24 4 24.996196 4.4473828
## .. ... ... ... ... ... ... ...## <!-- html table generated in R 3.2.3 by xtable 1.8-2 package -->
## <!-- Fri Feb 19 11:14:34 2016 -->
## <table border=1>
## <tr> <th> </th> <th> parent </th> <th> analyte </th> <th> matrix </th> <th> time </th> <th> count </th> <th> ConcMean </th> <th> ConcSD </th> </tr>
## <tr> <td align="right"> 1 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 3.34 </td> <td align="right"> 1.18 </td> </tr>
## <tr> <td align="right"> 2 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 5.36 </td> <td align="right"> 2.75 </td> </tr>
## <tr> <td align="right"> 3 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 3.12 </td> <td align="right"> 1.26 </td> </tr>
## <tr> <td align="right"> 4 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 1.55 </td> <td align="right"> 0.61 </td> </tr>
## <tr> <td align="right"> 5 </td> <td> atrazine </td> <td> atrazine </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 1.00 </td> <td align="right"> 0.35 </td> </tr>
## <tr> <td align="right"> 6 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 15.93 </td> <td align="right"> 2.59 </td> </tr>
## <tr> <td align="right"> 7 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 19.03 </td> <td align="right"> 4.35 </td> </tr>
## <tr> <td align="right"> 8 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 18.77 </td> <td align="right"> 2.70 </td> </tr>
## <tr> <td align="right"> 9 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 20.61 </td> <td align="right"> 3.89 </td> </tr>
## <tr> <td align="right"> 10 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 25.00 </td> <td align="right"> 4.45 </td> </tr>
## <tr> <td align="right"> 11 </td> <td> atrazine </td> <td> atrazine </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 26.43 </td> <td align="right"> 4.38 </td> </tr>
## <tr> <td align="right"> 12 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 13 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.03 </td> </tr>
## <tr> <td align="right"> 14 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.05 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 15 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 16 </td> <td> atrazine </td> <td> dea </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 17 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 18 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 19 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 20 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 21 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 22 </td> <td> atrazine </td> <td> dea </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 23 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.33 </td> <td align="right"> 0.12 </td> </tr>
## <tr> <td align="right"> 24 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.94 </td> <td align="right"> 0.76 </td> </tr>
## <tr> <td align="right"> 25 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 1.08 </td> <td align="right"> 0.51 </td> </tr>
## <tr> <td align="right"> 26 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 1.99 </td> <td align="right"> 1.35 </td> </tr>
## <tr> <td align="right"> 27 </td> <td> atrazine </td> <td> dia </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.66 </td> <td align="right"> 0.53 </td> </tr>
## <tr> <td align="right"> 28 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 29 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> -0.01 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 30 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 31 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.07 </td> </tr>
## <tr> <td align="right"> 32 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.03 </td> </tr>
## <tr> <td align="right"> 33 </td> <td> atrazine </td> <td> dia </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.06 </td> <td align="right"> 0.06 </td> </tr>
## <tr> <td align="right"> 34 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 1.87 </td> <td align="right"> 1.35 </td> </tr>
## <tr> <td align="right"> 35 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 1.30 </td> <td align="right"> 0.52 </td> </tr>
## <tr> <td align="right"> 36 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.57 </td> <td align="right"> 0.24 </td> </tr>
## <tr> <td align="right"> 37 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.27 </td> <td align="right"> 0.05 </td> </tr>
## <tr> <td align="right"> 38 </td> <td> fipronil </td> <td> fipronil </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.21 </td> <td align="right"> 0.13 </td> </tr>
## <tr> <td align="right"> 39 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 8 </td> <td align="right"> 0.41 </td> <td align="right"> 0.45 </td> </tr>
## <tr> <td align="right"> 40 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.87 </td> <td align="right"> 0.24 </td> </tr>
## <tr> <td align="right"> 41 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.82 </td> <td align="right"> 0.17 </td> </tr>
## <tr> <td align="right"> 42 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.70 </td> <td align="right"> 0.11 </td> </tr>
## <tr> <td align="right"> 43 </td> <td> fipronil </td> <td> fipronil </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.36 </td> <td align="right"> 0.06 </td> </tr>
## <tr> <td align="right"> 44 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.35 </td> <td align="right"> 0.29 </td> </tr>
## <tr> <td align="right"> 45 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.40 </td> <td align="right"> 0.48 </td> </tr>
## <tr> <td align="right"> 46 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.61 </td> <td align="right"> 0.57 </td> </tr>
## <tr> <td align="right"> 47 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 1.25 </td> <td align="right"> 0.53 </td> </tr>
## <tr> <td align="right"> 48 </td> <td> fipronil </td> <td> fipsulf </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.91 </td> <td align="right"> 0.57 </td> </tr>
## <tr> <td align="right"> 49 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 8 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 50 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 51 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 52 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 53 </td> <td> fipronil </td> <td> fipsulf </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 54 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.06 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 55 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.05 </td> </tr>
## <tr> <td align="right"> 56 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 57 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 58 </td> <td> triadimefon </td> <td> tdla </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 59 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 60 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 61 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 62 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 63 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 64 </td> <td> triadimefon </td> <td> tdla </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 65 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.02 </td> </tr>
## <tr> <td align="right"> 66 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.13 </td> <td align="right"> 0.05 </td> </tr>
## <tr> <td align="right"> 67 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.08 </td> <td align="right"> 0.05 </td> </tr>
## <tr> <td align="right"> 68 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 69 </td> <td> triadimefon </td> <td> tdlb </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.03 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 70 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 0.00 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 71 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 72 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.01 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 73 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.00 </td> </tr>
## <tr> <td align="right"> 74 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.02 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 75 </td> <td> triadimefon </td> <td> tdlb </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.04 </td> <td align="right"> 0.01 </td> </tr>
## <tr> <td align="right"> 76 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 0.39 </td> <td align="right"> 0.08 </td> </tr>
## <tr> <td align="right"> 77 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 0.55 </td> <td align="right"> 0.30 </td> </tr>
## <tr> <td align="right"> 78 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 0.75 </td> <td align="right"> 0.32 </td> </tr>
## <tr> <td align="right"> 79 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 0.87 </td> <td align="right"> 0.86 </td> </tr>
## <tr> <td align="right"> 80 </td> <td> triadimefon </td> <td> triadimefon </td> <td> amphib </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 0.25 </td> <td align="right"> 0.08 </td> </tr>
## <tr> <td align="right"> 81 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right"> 0 </td> <td align="right"> 4 </td> <td align="right"> 3.11 </td> <td align="right"> 0.85 </td> </tr>
## <tr> <td align="right"> 82 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right"> 2 </td> <td align="right"> 4 </td> <td align="right"> 3.66 </td> <td align="right"> 1.34 </td> </tr>
## <tr> <td align="right"> 83 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right"> 4 </td> <td align="right"> 4 </td> <td align="right"> 5.28 </td> <td align="right"> 0.37 </td> </tr>
## <tr> <td align="right"> 84 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right"> 12 </td> <td align="right"> 4 </td> <td align="right"> 5.93 </td> <td align="right"> 1.00 </td> </tr>
## <tr> <td align="right"> 85 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right"> 24 </td> <td align="right"> 4 </td> <td align="right"> 4.82 </td> <td align="right"> 0.32 </td> </tr>
## <tr> <td align="right"> 86 </td> <td> triadimefon </td> <td> triadimefon </td> <td> soil </td> <td align="right"> 48 </td> <td align="right"> 4 </td> <td align="right"> 4.18 </td> <td align="right"> 0.44 </td> </tr>
## </table>The amphibian data set summary statistics. Atrazine peaks at 4 hours and then declines monotonically. DEA peaks at 12 hours and DIA at 24. Fipronil steadily declines from its first observation at 2 hours with fipronil sulfone not peaking until 24 hours. Triadimenon peaks at 24 hours with its metabolites tdla and tdlb peaking at 4 hours.
## Classes 'grouped_df', 'tbl_df', 'tbl' and 'data.frame': 86 obs. of 7 variables:
## $ parent : Factor w/ 3 levels "atrazine","fipronil",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ analyte : Factor w/ 8 levels "atrazine","dea",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ matrix : Factor w/ 2 levels "amphib","soil": 1 1 1 1 1 2 2 2 2 2 ...
## $ time : int 2 4 12 24 48 0 2 4 12 24 ...
## $ count : int 4 4 4 4 4 4 4 4 4 4 ...
## $ ConcMean: num 3.34 5.36 3.12 1.55 1 ...
## $ ConcSD : num 1.175 2.752 1.257 0.61 0.355 ...
## - attr(*, "vars")=List of 3
## ..$ : symbol parent
## ..$ : symbol analyte
## ..$ : symbol matrix
## - attr(*, "drop")= logi TRUE## Source: local data frame [6 x 7]
## Groups: parent, analyte, matrix [2]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 atrazine atrazine amphib 2 4 3.33787563 1.17532253
## 2 atrazine atrazine amphib 4 4 5.35904387 2.75189034
## 3 atrazine atrazine amphib 12 4 3.12381130 1.25662887
## 4 atrazine atrazine amphib 24 4 1.55491895 0.60961016
## 5 atrazine atrazine amphib 48 4 1.00188749 0.35454734
## 6 atrazine dea amphib 2 4 0.01389877 0.00522407## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 atrazine atrazine amphib 2 4 3.33787563 1.17532253
## 2 atrazine atrazine amphib 4 4 5.35904387 2.75189034
## 3 atrazine atrazine amphib 12 4 3.12381130 1.25662887
## 4 atrazine atrazine amphib 24 4 1.55491895 0.60961016
## 5 atrazine atrazine amphib 48 4 1.00188749 0.35454734
## 6 atrazine dea amphib 2 4 0.01389877 0.00522407
## 7 atrazine dea amphib 4 4 0.04436711 0.02843181
## 8 atrazine dea amphib 12 4 0.05402182 0.01282235
## 9 atrazine dea amphib 24 4 0.03652473 0.01310278
## 10 atrazine dea amphib 48 4 0.01951501 0.01958540
## 11 atrazine dia amphib 2 4 0.32878185 0.12495746
## 12 atrazine dia amphib 4 4 0.94192818 0.76074427
## 13 atrazine dia amphib 12 4 1.08350960 0.50576827
## 14 atrazine dia amphib 24 4 1.98835970 1.34925248
## 15 atrazine dia amphib 48 4 0.66238821 0.53051448## [1] "atrazine"
## [1] "dea"
## [1] "dia"## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 fipronil fipronil amphib 2 4 1.8670398 1.34631230
## 2 fipronil fipronil amphib 4 4 1.3005836 0.52188454
## 3 fipronil fipronil amphib 12 4 0.5659565 0.24026633
## 4 fipronil fipronil amphib 24 4 0.2676732 0.05106111
## 5 fipronil fipronil amphib 48 4 0.2119504 0.13140536
## 6 fipronil fipsulf amphib 2 4 0.3465734 0.28711156
## 7 fipronil fipsulf amphib 4 4 0.3966089 0.47739157
## 8 fipronil fipsulf amphib 12 4 0.6129114 0.57346517
## 9 fipronil fipsulf amphib 24 4 1.2528179 0.52648677
## 10 fipronil fipsulf amphib 48 4 0.9067126 0.56596417## Source: local data frame [0 x 7]
## Groups: parent, analyte, matrix [0]
##
## Variables not shown: parent (fctr), analyte (fctr), matrix (fctr), time
## (int), count (int), ConcMean (dbl), ConcSD (dbl)The soil data set summary statistics. Atrazine in soil showing an upwards trend (need to test if significant) with dia and dea levels very low indicating little degradation in soil over the 48 hour period. Fipronil and triadimenon data also indicating little degradation in soil.
## Source: local data frame [18 x 7]
## Groups: parent, analyte, matrix [3]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 atrazine atrazine soil 0 4 15.930919692 2.591104068
## 2 atrazine atrazine soil 2 4 19.029034412 4.353430337
## 3 atrazine atrazine soil 4 4 18.770091080 2.695315758
## 4 atrazine atrazine soil 12 4 20.614190363 3.891851074
## 5 atrazine atrazine soil 24 4 24.996195532 4.447382801
## 6 atrazine atrazine soil 48 4 26.434744900 4.377099498
## 7 atrazine dea soil 0 4 0.000000000 0.000000000
## 8 atrazine dea soil 2 4 0.001570429 0.000633009
## 9 atrazine dea soil 4 4 0.002999216 0.001537652
## 10 atrazine dea soil 12 4 0.005469015 0.004234880
## 11 atrazine dea soil 24 4 0.007308439 0.001736211
## 12 atrazine dea soil 48 4 0.008784632 0.003772339
## 13 atrazine dia soil 0 4 0.000000000 0.000000000
## 14 atrazine dia soil 2 4 -0.007727286 0.007374085
## 15 atrazine dia soil 4 4 0.020538600 0.020166308
## 16 atrazine dia soil 12 4 0.077036921 0.067772652
## 17 atrazine dia soil 24 4 0.042975804 0.030007793
## 18 atrazine dia soil 48 4 0.063693292 0.058241606## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 fipronil fipronil soil 2 8 0.40768123 0.447265792
## 2 fipronil fipronil soil 4 4 0.86826316 0.244191727
## 3 fipronil fipronil soil 12 4 0.81738069 0.169691335
## 4 fipronil fipronil soil 24 4 0.70225877 0.108745058
## 5 fipronil fipronil soil 48 4 0.35560948 0.058543752
## 6 fipronil fipsulf soil 2 8 0.01022479 0.012898421
## 7 fipronil fipsulf soil 4 4 0.02193831 0.010765665
## 8 fipronil fipsulf soil 12 4 0.01829893 0.005013814
## 9 fipronil fipsulf soil 24 4 0.01917848 0.009139211
## 10 fipronil fipsulf soil 48 4 0.01262887 0.005517408## Source: local data frame [0 x 7]
## Groups: parent, analyte, matrix [0]
##
## Variables not shown: parent (fctr), analyte (fctr), matrix (fctr), time
## (int), count (int), ConcMean (dbl), ConcSD (dbl)pdf(paste(micro.graphics,"data_mean_scatterplot",".pdf", sep=""))
par(mfrow=c(3,1))
print(parents)## [1] atrazine triadimefon fipronil
## Levels: atrazine fipronil triadimefon for(parent in parents){
i=0
print(parent)
temp.parent <- micro.group.stats.amphib[which(micro.group.stats.amphib$parent==parent),]
print(temp.parent)
parent.analytes <- unique(temp.parent$analyte)
for(analyte in parent.analytes){
print(parent)
print(analyte)
analytetemp <- micro.group.stats.amphib[which(micro.group.stats.amphib$analyte==analyte),]
xvalues <- as.numeric(as.character(analytetemp$time))
points.y <- micro.amphib[which(micro.amphib$analyte==analyte),]$conc
points.x <- as.numeric(as.character(micro.amphib[which(micro.amphib$analyte==analyte),]$time))
#create empty plot if needed
if(i==0){
parenttemp <- micro.group.stats.amphib[which(micro.group.stats.amphib$parent==parent),]
maxconc <- max(points.y)
plot(xvalues,analytetemp$ConcMean,type="l", xlim=c(0,48),
ylim = c(0,maxconc), main=parent,col="black", xlab="Hours", ylab="Concentration")
axis(1,at=xvalues)
i=1
}
#add line for parent metabolite
if(analyte %in% parents){
lines(xvalues,analytetemp$ConcMean,type="l",col="red")
points(points.x, points.y, col = "red")
}else{
#add line for daughter metabolite
lines(xvalues,analytetemp$ConcMean,type="l",col="blue")
points(points.x, points.y, col = "blue")
}
}
}## [1] "atrazine"
## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 atrazine atrazine amphib 2 4 3.33787563 1.17532253
## 2 atrazine atrazine amphib 4 4 5.35904387 2.75189034
## 3 atrazine atrazine amphib 12 4 3.12381130 1.25662887
## 4 atrazine atrazine amphib 24 4 1.55491895 0.60961016
## 5 atrazine atrazine amphib 48 4 1.00188749 0.35454734
## 6 atrazine dea amphib 2 4 0.01389877 0.00522407
## 7 atrazine dea amphib 4 4 0.04436711 0.02843181
## 8 atrazine dea amphib 12 4 0.05402182 0.01282235
## 9 atrazine dea amphib 24 4 0.03652473 0.01310278
## 10 atrazine dea amphib 48 4 0.01951501 0.01958540
## 11 atrazine dia amphib 2 4 0.32878185 0.12495746
## 12 atrazine dia amphib 4 4 0.94192818 0.76074427
## 13 atrazine dia amphib 12 4 1.08350960 0.50576827
## 14 atrazine dia amphib 24 4 1.98835970 1.34925248
## 15 atrazine dia amphib 48 4 0.66238821 0.53051448
## [1] "atrazine"
## [1] "atrazine"## [1] "atrazine"
## [1] "dea"
## [1] "atrazine"
## [1] "dia"
## [1] "triadimefon"
## Source: local data frame [15 x 7]
## Groups: parent, analyte, matrix [3]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 triadimefon tdla amphib 2 4 0.05514470 0.021089764
## 2 triadimefon tdla amphib 4 4 0.08150175 0.046221502
## 3 triadimefon tdla amphib 12 4 0.03632384 0.015222899
## 4 triadimefon tdla amphib 24 4 0.02400790 0.007522554
## 5 triadimefon tdla amphib 48 4 0.01549908 0.004845715
## 6 triadimefon tdlb amphib 2 4 0.08362714 0.016364595
## 7 triadimefon tdlb amphib 4 4 0.13009543 0.054315693
## 8 triadimefon tdlb amphib 12 4 0.07664673 0.048553355
## 9 triadimefon tdlb amphib 24 4 0.04183235 0.011652266
## 10 triadimefon tdlb amphib 48 4 0.02950214 0.003438978
## 11 triadimefon triadimefon amphib 2 4 0.38678831 0.075852995
## 12 triadimefon triadimefon amphib 4 4 0.54862458 0.300394386
## 13 triadimefon triadimefon amphib 12 4 0.75491439 0.318237965
## 14 triadimefon triadimefon amphib 24 4 0.86540039 0.860421208
## 15 triadimefon triadimefon amphib 48 4 0.24868748 0.079848623
## [1] "triadimefon"
## [1] "tdla"## [1] "triadimefon"
## [1] "tdlb"
## [1] "triadimefon"
## [1] "triadimefon"
## [1] "fipronil"
## Source: local data frame [10 x 7]
## Groups: parent, analyte, matrix [2]
##
## parent analyte matrix time count ConcMean ConcSD
## (fctr) (fctr) (fctr) (int) (int) (dbl) (dbl)
## 1 fipronil fipronil amphib 2 4 1.8670398 1.34631230
## 2 fipronil fipronil amphib 4 4 1.3005836 0.52188454
## 3 fipronil fipronil amphib 12 4 0.5659565 0.24026633
## 4 fipronil fipronil amphib 24 4 0.2676732 0.05106111
## 5 fipronil fipronil amphib 48 4 0.2119504 0.13140536
## 6 fipronil fipsulf amphib 2 4 0.3465734 0.28711156
## 7 fipronil fipsulf amphib 4 4 0.3966089 0.47739157
## 8 fipronil fipsulf amphib 12 4 0.6129114 0.57346517
## 9 fipronil fipsulf amphib 24 4 1.2528179 0.52648677
## 10 fipronil fipsulf amphib 48 4 0.9067126 0.56596417
## [1] "fipronil"
## [1] "fipronil"## [1] "fipronil"
## [1] "fipsulf"dev.off()## quartz_off_screen
## 2la de da
turn times series to zoo objects
estimate lambdas using maximum likelihood for each time series
library(maxLik)
MLexp <- function(times, data){
expLik <- function(param) { y <- data t <- times alpha1 <- param[1] lambda1 <- param[2]-1(alpha1-lambda1t) - y/(exp(alpha1-lambda1*t)) }
max.fit <- maxLik(expLik, start = c(1,1)) crit <- qt(.975, length(data)-2) max.intercept.CI <- c(summary(max.fit)\(est[1,1]-crit*summary(max.fit)\)est[1,2],summary(max.fit)\(est[1,1]+crit*summary(max.fit)\)est[1,2]) max.decayrate.CI <- c(-1summary(max.fit)\(est[2,1]-crit*summary(max.fit)\)est[2,2],-1summary(max.fit)\(est[2,1]+crit*summary(max.fit)\)est[2,2]) max.halflife.CI <- c(log(2)/max.decayrate.CI[2],log(2)/max.decayrate.CI[1])
paste(“MLE for Initial Concentration =”,max.fit\(est[1], "MLE for decay rate =", max.fit\)est[2], “MLE for half life =”, -log(.5)/max.fit$est[2])
temp.list <- list(max.fit\(est[1], max.fit\)est[2], -log(.5)/max.fit$est[2], max.intercept.CI, max.decayrate.CI, max.halflife.CI, vcov(max.fit) ) return(temp.list) }
MLexp.intercept <- function(times, data) { temp.fit <- MLexp(times,data) temp.fit[[1]] }
MLexp.decayrate <- function(times, data) { temp.fit <- MLexp(times,data) temp.fit[[2]] }
MLexp.halflife <- function(times,data) { temp.fit <- MLexp(times,data) temp.fit[[3]] }
MLexp.intercept.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[4]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }
MLexp.decayrate.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[5]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }
MLexp.halflife.CI <- function(times,data){ temp.fit <- MLexp(times,data) temp2 <- temp.fit[[6]] names(temp2) <- c(“Lower95”, “Upper95”) temp2 }
microsome experiment analysis
data in csv format